Metamaterial surfaces

ABSTRACT

An apparatus to modify an incident free space electromagnetic wave includes a block of an artificially structured material having an adjustable spatial distribution of electromagnetic parameters (e.g., ∈, μ, η, σ, and n). A controller applies control signals to dynamically adjust the spatial distribution of electromagnetic parameters in the material to introduce a time-varying path delay d (t) in the modified electromagnetic wave relative to the incident electromagnetic wave.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is related to and claims the benefit of theearliest available effective filing date(s) from the following listedapplication(s) (the “Related Applications”) (e.g., claims earliestavailable priority dates for other than provisional patent applicationsor claims benefits under 35 USC §119(e) for provisional patentapplications, for any and all parent, grandparent, great-grandparent,etc. applications of the Related Application(s)). All subject matter ofthe Related Applications and of any and all parent, grandparent,great-grandparent, etc. applications of the Related Applications isincorporated herein by reference to the extent such subject matter isnot inconsistent herewith.

RELATED APPLICATIONS

-   -   1. For purposes of the USPTO extra-statutory requirements, the        present application is related to U.S. patent application Ser.        No. 12/386,522, entitled EVANESCENT ELECTROMAGNETIC WAVE        CONVERSION APPARATUS I, naming Jeffrey A. Bowers, Roderick A.        Hyde, Edward K. Y. Jung, John Brian Pendry, David Schurig,        David R. Smith, Clarence T. Tegreene, Thomas Allan Weaver,        Charles Whitmer, Lowell L. Wood, Jr. as inventors, filed Apr.        17, 2009, which is currently co-pending, or is an application of        which a currently co-pending application is entitled to the        benefit of the filing date.    -   2. For purposes of the USPTO extra-statutory requirements, the        present application is related to U.S. patent application Ser.        No. 12/386,523, entitled EVANESCENT ELECTROMAGNETIC WAVE        CONVERSION APPARATUS H, naming Jeffrey A. Bowers, Roderick A.        Hyde, Edward K. Y. Jung, John Brian Pendry, David Schurig,        David R. Smith, Clarence T. Tegreene, Thomas Allan Weaver,        Charles Whitmer, Lowell L. Wood, Jr. as inventors, filed Apr.        17, 2009, which is currently co-pending, or is an application of        which a currently co-pending application is entitled to the        benefit of the filing date.    -   3. For purposes of the USPTO extra-statutory requirements, the        present application is related to U.S. patent application Ser.        No. 12/386,521, entitled EVANESCENT ELECTROMAGNETIC WAVE        CONVERSION APPARATUS III, naming Jeffrey A. Bowers, Roderick A.        Hyde, Edward K. Y. Jung, John Brian Pendry, David Schurig,        David R. Smith, Clarence T. Tegreene, Thomas Allan Weaver,        Charles Whitmer, Lowell L. Wood, Jr. as inventors, filed Apr.        17, 2009, which is currently co-pending, or is an application of        which a currently co-pending application is entitled to the        benefit of the filing date.

The United States Patent Office (USPTO) has published a notice to theeffect that the USPTO's computer programs require that patent applicantsreference both a serial number and indicate whether an application is acontinuation or continuation-in-part. Stephen G. Kunin, Benefit ofPrior-Filed Application, USPTO Official Gazette Mar. 18, 2003. Thepresent Applicant Entity (hereinafter “Applicant”) has provided above aspecific reference to the application(s) from which priority is beingclaimed as recited by statute. Applicant understands that the statute isunambiguous in its specific reference language and does not requireeither a serial number or any characterization, such as “continuation”or “continuation-in-part,” for claiming priority to U.S. patentapplications. Notwithstanding the foregoing, Applicant understands thatthe USPTO's computer programs have certain data entry requirements, andhence Applicant is designating the present application as acontinuation-in-part of its parent applications as set forth above, butexpressly points out that such designations are not to be construed inany way as any type of commentary and/or admission as to whether or notthe present application contains any new matter in addition to thematter of its parent application(s).

TECHNICAL FIELD

This disclosure relates to apparatus and methods for tailored orengineered responses to electromagnetic waves. The apparatus and methodsare based on artificially-structured materials (e.g., metamaterials orbroadband metamaterials) or other materials that exhibit exceptionalproperties not readily observed in nature. The materials may exhibitqualitatively new response functions that are observed in theconstituent materials, which may result from the inclusion ofartificially fabricated, extrinsic, low dimensional inhomogeneities. Thenew properties may emerge due to specific interactions withelectromagnetic fields or due to external electrical control.

BRIEF DESCRIPTION OF THE FIGURES

In the accompanying drawings:

FIGS. 1 and 2 are schematic diagrams illustrating an exemplaryapparatus, which is configured to modify an incident free spaceelectromagnetic wave, in accordance with the principles of the solutionsdescribed herein;

FIGS. 3 and 4 are schematic diagrams illustrating an exemplary variablereflector made of artificially-structured elements, in accordance withthe principles of the solutions described herein

FIGS. 5 and 6 are schematic diagrams illustrating an exemplary variablephase or time delay made of artificially-structured transmissiveelements, in accordance with the principles of the solutions describedherein;

FIG. 7 is a schematic diagrams illustrating an exemplary variable phaseor time delay made of an artificially structured material having acontrollable index of refraction responsive to an applied field (F), inaccordance with the principles of the solutions described herein; and

FIGS. 8-11 are flow diagrams illustrating exemplary features of methodsthat modify incident electromagnetic waves, in accordance with theprinciples of the solutions described herein.

FIGS. 12A-E, 13, 14A and 14B, 15 and 16A-F are schematic diagrams whichillustrate exemplary modifications of incident electromagnetic waves bythe apparatus of FIGS. 1-7 and/or the methods of FIGS. 8-11, inaccordance with the principles of the solutions described herein.

Throughout the figures, unless otherwise stated, the same referencenumerals and characters are used to denote like features, elements,components, or portions of the illustrated embodiments.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented here. Some embodiments provide an indefinite medium that is atransformation medium, i.e. an electromagnetic medium having propertiesthat may be characterized according to transformation optics.

Transformation optics is an emerging field of electromagneticengineering, and transformation optics devices include structures thatinfluence electromagnetic waves, where the influencing imitates thebending of electromagnetic waves in a curved coordinate space (a“transformation” of a flat coordinate space), e.g. as described in A. J.Ward and J. B. Pendry, “Refraction and geometry in Maxwell's equations,”J. Mod. Optics 43, 773 (1996), J. B. Pendry and S. A. Ramakrishna,“Focusing light using negative refraction,” J. Phys. [Cond. Matt.] 15,6345 (2003), D. Schurig et al, “Calculation of material properties andray tracing in transformation media,” Optics Express 14, 9794 (2006)(“D. Schurig et al (1)”), and in U. Leonhardt and T. G. Philbin,“General relativity in electrical engineering,” New J. Phys. 8, 247(2006), each of which is herein incorporated by reference. The use ofthe term “optics” does not imply any limitation with regards towavelength; a transformation optics device may be operable in wavelengthbands that range from radio wavelengths to visible wavelengths andbeyond.

A first exemplary transformation optics device is the electromagneticcloak that was described, simulated, and implemented, respectively, inJ. B. Pendry et al, “Controlling electromagnetic waves,” Science 312,1780 (2006); S. A. Cummer et al, “Full-wave simulations ofelectromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006);and D. Schurig et al, “Metamaterial electromagnetic cloak at microwavefrequencies,” Science 314, 977 (2006) (“D. Schurig et al (2)”); each ofwhich is herein incorporated by reference. See also J. Pendry et al,“Electromagnetic cloaking method,” U.S. patent application Ser. No.11/459,728, herein incorporated by reference. For the electromagneticcloak, the curved coordinate space is a transformation of a flat spacethat has been punctured and stretched to create a hole (the cloakedregion), and this transformation corresponds to a set of constitutiveparameters (electric permittivity and magnetic permeability) for atransformation medium wherein electromagnetic waves are refracted aroundthe hole in imitation of the curved coordinate space.

A second exemplary transformation optics device is illustrated byembodiments of the electromagnetic compression structure described in J.B. Pendry, D. Schurig, and D. R. Smith, “Electromagnetic compressionapparatus, methods, and systems,” U.S. patent application Ser. No.11/982,353; and in J. B. Pendry, D. Schurig, and D. R. Smith,“Electromagnetic compression apparatus, methods, and systems,” U.S.patent application Ser. No. 12/069,170; each of which is hereinincorporated by reference. In embodiments described therein, anelectromagnetic compression structure includes a transformation mediumwith constitutive parameters corresponding to a coordinatetransformation that compresses a region of space intermediate first andsecond spatial locations, the effective spatial compression beingapplied along an axis joining the first and second spatial locations.The electromagnetic compression structure thereby provides an effectiveelectromagnetic distance between the first and second spatial locationsgreater than a physical distance between the first and second spatiallocations.

A third exemplary transformation optics device is illustrated byembodiments of the electromagnetic cloaking and/or translation structuredescribed in J. T. Kare, “Electromagnetic cloaking apparatus, methods,and systems,” U.S. patent application Ser. No. 12/074,247; and in J. T.Kare, “Electromagnetic cloaking apparatus, methods, and systems,” U.S.patent application Ser. No. 12/074,248; each of which is hereinincorporated by reference. In embodiments described therein, anelectromagnetic translation structure includes a transformation mediumthat provides an apparent location of an electromagnetic transducerdifferent then an actual location of the electromagnetic transducer,where the transformation medium has constitutive parameterscorresponding to a coordinate transformation that maps the actuallocation to the apparent location. Alternatively or additionally,embodiments include an electromagnetic cloaking structure operable todivert electromagnetic radiation around an obstruction in a field ofregard of the transducer (and the obstruction can be anothertransducer).

A fourth exemplary transformation optics device is illustrated byembodiments of the various focusing and/or focus-adjusting structuresdescribed in J. A. Bowers et al, “Focusing and sensing apparatus,methods, and systems,” U.S. patent application Ser. No. 12/156,443; J.A. Bowers et al, “Emitting and focusing apparatus, methods, andsystems,” U.S. patent application Ser. No. 12/214,534; J. A. Bowers etal, “Negatively-refractive focusing and sensing apparatus, methods, andsystems,” U.S. patent application Ser. No. 12/220,705; J. A. Bowers etal, “Emitting and negatively-refractive focusing apparatus, methods, andsystems,” U.S. patent application Ser. No. 12/220,703; J. A. Bowers etal, “Negatively-refractive focusing and sensing apparatus, methods, andsystems,” U.S. patent application Ser. No. 12/228,140; and J. A. Bowerset al, “Emitting and negatively-refractive focusing apparatus, methods,and systems,” U.S. patent application Ser. No. 12/228,153; each of whichis herein incorporated by reference. In embodiments described therein, afocusing and/or focusing-structure includes a transformation medium thatprovides an extended depth of focus/field greater than a nominal depthof focus/field, or an interior focus/field region with an axialmagnification that is substantially greater than or less than one.

Additional exemplary transformation optics devices are described in D.Schurig et al, “Transformation-designed optical elements,” Opt. Exp. 15,14772 (2007); M. Rahm et al, “Optical design of reflectionless complexmedia by finite embedded coordinate transformations,” Phys. Rev. Lett.100, 063903 (2008); and A. Kildishev and V. Shalaev, “Engineering spacefor light via transformation optics,” Opt. Lett. 33, 43 (2008); each ofwhich is herein incorporated by reference. In general, for a selectedcoordinate transformation, a transformation medium can be identifiedwherein electromagnetic fields evolve as in a curved coordinate spacecorresponding to the selected coordinate transformation. Constitutiveparameters of the transformation medium can be obtained from theequations:

{tilde over (∈)}^(i′j′)=[det(Λ)]⁻¹Λ_(i) ^(i′)Λ_(j) ^(j′)∈^(ij)  (1)

{tilde over (μ)}^(i′j′)=[det(Λ)]⁻¹Λ_(i) ^(i′)Λ_(j) ^(j′)μ^(ij)  (2)

where {tilde over (∈)} and {tilde over (μ)} are the permittivity andpermeability tensors of the transformation medium, ∈ and μ are thepermittivity and permeability tensors of the original medium in theuntransformed coordinate space, and

$\begin{matrix}{\Lambda_{i}^{i^{\prime}} = \frac{\partial x^{i^{\prime}}}{\partial x^{i}}} & (3)\end{matrix}$

is the Jacobian matrix corresponding to the coordinate transformation.In some applications, the coordinate transformation is a one-to-onemapping of locations in the untransformed coordinate space to locationsin the transformed coordinate space, and in other applications thecoordinate transformation is a one-to-many mapping of locations in theuntransformed coordinate space to locations in the transformedcoordinate space. Some coordinate transformations, such as one-to-manymappings, may correspond to a transformation medium having a negativeindex of refraction. In some applications, the transformation medium isan indefinite medium, i.e. an electromagnetic medium having anindefinite permittivity and/or an indefinite permeability (thesetransformation media may be referred to as “indefinite transformationmedia”). For example, in equations (1) and (2), if the originalpermittivity matrix ∈ is indefinite, then the transformed permittivitymatrix {tilde over (∈)} is also indefinite; and/or if the originalpermeability matrix μ is indefinite, then the transformed permeabilitymatrix {tilde over (μ)} is also indefinite. In some applications, onlyselected matrix elements of the permittivity and permeability tensorsneed satisfy equations (1) and (2), e.g. where the transformation opticsresponse is for a selected polarization only. In other applications, afirst set of permittivity and permeability matrix elements satisfyequations (1) and (2) with a first Jacobian Λ, corresponding to a firsttransformation optics response for a first polarization ofelectromagnetic waves, and a second set of permittivity and permeabilitymatrix elements, orthogonal (or otherwise complementary) to the firstset of matrix elements, satisfy equations (1) and (2) with a secondJacobian Λ′, corresponding to a second transformation optics responsefor a second polarization of electromagnetic waves. In yet otherapplications, reduced parameters are used that may not satisfy equations(1) and (2), but preserve products of selected elements in (1) andselected elements in (2), thus preserving dispersion relations insidethe transformation medium (see, for example, D. Schurig et al (2),supra, and W. Cai et al, “Optical cloaking with metamaterials,” NaturePhotonics 1, 224 (2007), herein incorporated by reference). Reducedparameters can be used, for example, to substitute a magnetic responsefor an electric response, or vice versa. While reduced parameterspreserve dispersion relations inside the transformation medium (so thatthe ray or wave trajectories inside the transformation medium areunchanged from those of equations (1) and (2)), they may not preserveimpedance characteristics of the transformation medium, so that rays orwaves incident upon a boundary or interface of the transformation mediummay sustain reflections (whereas in general a transformation mediumaccording to equations (1) and (2) is substantially nonreflective orsustains the reflection characteristics of the original medium in theuntransformed coordinate space). The reflective or scatteringcharacteristics of a transformation medium with reduced parameters canbe substantially reduced or eliminated (modulo any reflectioncharacteristics of the original medium in the untransformed coordinatespace) by a suitable choice of coordinate transformation, e.g. byselecting a coordinate transformation for which the correspondingJacobian Λ (or a subset of elements thereof) is continuous orsubstantially continuous at a boundary or interface of thetransformation medium (see, for example, W. Cai et al, “Nonmagneticcloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007),herein incorporated by reference).

Embodiments of an indefinite medium and/or a transformation medium(including embodiments of indefinite transformation media) can berealized using the artificially-structured materials. Generallyspeaking, the electromagnetic properties of the artificially-structuredmaterials derive from their structural configurations, rather than or inaddition to their material composition.

In some embodiments, the artificially-structured materials are photoniccrystals. Some exemplary photonic crystals are described in J. D.Joannopoulos et al, Photonic Crystals Molding the Flow of Light, 2^(nd)Edition, Princeton Univ. Press, 2008, which is incorporated by referenceherein. In a photonic crystals, photonic dispersion relations and/orphotonic band gaps are engineered by imposing a spatially-varyingpattern on an electromagnetic material (e.g. a conducting, magnetic, ordielectric material) or a combination of electromagnetic materials. Thephotonic dispersion relations translate to effective constitutiveparameters (e.g. permittivity, permeability, index of refraction) forthe photonic crystal. The spatially-varying pattern is typicallyperiodic, quasi-periodic, or colloidal periodic, with a length scalecomparable to an operating wavelength of the photonic crystal.

In other embodiments, the artificially-structured materials aremetamaterials. Some exemplary metamaterials are described in R. A. Hydeet al, “Variable metamaterial apparatus,” U.S. patent application Ser.No. 11/355,493; D. Smith et al, “Metamaterials,” InternationalApplication No. PCT/US2005/026052; D. Smith et al, “Metamaterials andnegative refractive index,” Science 305, 788 (2004); D. Smith et al,“Indefinite materials,” U.S. patent application Ser. No. 10/525,191; C.Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission LineTheory and Microwave Applications, Wiley-Interscience, 2006; N. Enghetaand R. W. Ziolkowski, eds., Metamaterials: Physics and EngineeringExplorations, Wiley-Interscience, 2006; and A. K. Sarychev and V. M.Shalaev, Electrodynamics of Metamaterials, World Scientific, 2007; eachof which is herein incorporated by reference.

Metamaterials generally feature subwavelength elements, i.e. structuralelements with portions having electromagnetic length scales smaller thanan operating wavelength of the metamaterial, and the subwavelengthelements have a collective response to electromagnetic radiation thatcorresponds to an effective continuous medium response, characterized byan effective permittivity, an effective permeability, an effectivemagnetoelectric coefficient, or any combination thereof. For example,the electromagnetic radiation may induce charges and/or currents in thesubwavelength elements, whereby the subwavelength elements acquirenonzero electric and/or magnetic dipole moments. Where the electriccomponent of the electromagnetic radiation induces electric dipolemoments, the metamaterial has an effective permittivity; where themagnetic component of the electromagnetic radiation induces magneticdipole moments, the metamaterial has an effective permeability; andwhere the electric (magnetic) component induces magnetic (electric)dipole moments (as in a chiral metamaterial), the metamaterial has aneffective magnetoelectric coefficient. Some metamaterials provide anartificial magnetic response; for example, split-ring resonators(SRRs)—or other LC or plasmonic resonators—built from nonmagneticconductors can exhibit an effective magnetic permeability (c.f. J. B.Pendry et al, “Magnetism from conductors and enhanced nonlinearphenomena,” IEEE Trans. Micro. Theo. Tech. 47, 2075 (1999), hereinincorporated by reference). Some metamaterials have “hybrid”electromagnetic properties that emerge partially from structuralcharacteristics of the metamaterial, and partially from intrinsicproperties of the constituent materials. For example, G. Dewar, “A thinwire array and magnetic host structure with n<0,” J. Appl. Phys. 97,10Q101 (2005), herein incorporated by reference, describes ametamaterial consisting of a wire array (exhibiting a negativepermeability as a consequence of its structure) embedded in anonconducting ferrimagnetic host medium (exhibiting an intrinsicnegative permeability). Metamaterials can be designed and fabricated toexhibit selected permittivities, permeabilities, and/or magnetoelectriccoefficients that depend upon material properties of the constituentmaterials as well as shapes, chiralities, configurations, positions,orientations, and couplings between the subwavelength elements. Theselected permittivites, permeabilities, and/or magnetoelectriccoefficients can be positive or negative, complex (having loss or gain),anisotropic, variable in space (as in a gradient index lens), variablein time (e.g. in response to an external or feedback signal), variablein frequency (e.g. in the vicinity of a resonant frequency of themetamaterial), or any combination thereof. The selected electromagneticproperties can be provided at wavelengths that range from radiowavelengths to infrared/visible wavelengths; the latter wavelengths areattainable, e.g., with nanostructured materials such as nanorod pairs ornano-fishnet structures (c.f. S. Linden et al, “Photonic metamaterials:Magnetism at optical frequencies,” IEEE J. Select. Top. Quant. Elect.12, 1097 (2006) and V. Shalaev, “Optical negative-index metamaterials,”Nature Photonics 1, 41 (2007), both herein incorporated by reference).An example of a three-dimensional metamaterial at optical frequencies,an elongated-split-ring “woodpile” structure, is described in M. S. Rillet al, “Photonic metamaterials by direct laser writing and silverchemical vapour deposition,” Nature Materials advance onlinepublication, May 11, 2008, (doi:10.1038/nmat2197).

While many exemplary metamaterials are described as including discreteelements, some implementations of metamaterials may include non-discreteelements or structures. For example, a metamaterial may include elementscomprised of sub-elements, where the sub-elements are discretestructures (such as split-ring resonators, etc.), or the metamaterialmay include elements that are inclusions, exclusions, layers, or othervariations along some continuous structure (e.g. etchings on asubstrate). Some examples of layered metamaterials include: a structureconsisting of alternating doped/intrinsic semiconductor layers (cf. A.J. Hoffman, “Negative refraction in semiconductor metamaterials,” NatureMaterials 6, 946 (2007), herein incorporated by reference), and astructure consisting of alternating metal/dielectric layers (cf. A.Salandrino and N. Engheta, “Far-field subdiffraction optical microscopyusing metamaterial crystals: Theory and simulations,” Phys. Rev. B 74,075103 (2006); and Z. Jacob et al, “Optical hyperlens: Far-field imagingbeyond the diffraction limit,” Opt. Exp. 14, 8247 (2006); each of whichis herein incorporated by reference). The metamaterial may includeextended structures having distributed electromagnetic responses (suchas distributed inductive responses, distributed capacitive responses,and distributed inductive-capacitive responses). Examples includestructures consisting of loaded and/or interconnected transmission lines(such as microstrips and striplines), artificial ground plane structures(such as artificial perfect magnetic conductor (PMC) surfaces andelectromagnetic band gap (EGB) surfaces), and interconnected/extendednanostructures (nano-fishnets, elongated SRR woodpiles, etc.).

While many exemplary metamaterials are described as including discreteelements, some implementations of metamaterials may include non-discreteelements or structures. For example, a metamaterial may include elementscomprised of sub-elements, where the sub-elements are discretestructures (such as split-ring resonators, etc.), or the metamaterialmay include elements that are inclusions, exclusions, or othervariations along some continuous structure (e.g. etchings on asubstrate). The metamaterial may include extended structures havingdistributed electromagnetic responses (such as distributed inductiveresponses, distributed capacitive responses, and distributedinductive-capacitive responses). Examples include structures consistingof loaded and/or interconnected transmission lines (such as microstripsand striplines), artificial ground plane structures (such as artificialperfect magnetic conductor (PMC) surfaces and electromagnetic band gap(EGB) surfaces), and interconnected/extended nanostructures(nano-fishnets, elongated SRR woodpiles, etc.).

In some embodiments a metamaterial may include a layered structure. Forexample, embodiments may provide a structure having a succession ofadjacent layers, where the layers have a corresponding succession ofmaterial properties that include electromagnetic properties (such aspermittivity and/or permeability). The succession of adjacent layers maybe an alternating or repeating succession of adjacent layers, e.g. astack of layers of a first type interleaved with layers of a secondtype, or a stack that repeats a sequence of three or more types oflayers. When the layers are sufficiently thin (e.g. having thicknessessmaller than an operating wavelength of the metamaterial), the layeredstructure may be characterized as an effective continuous medium havingeffective constitutive parameters that relate to the electromagneticproperties of the individual layers. For example, consider a planarstack of layers of a first material (of thickness d₁, and havinghomogeneous and isotropic electromagnetic parameters ∈₁, μ₁) interleavedwith layers of a second material (of thickness d₂, and havinghomogeneous and isotropic electromagnetic parameters ∈₂, μ₂); then thelayered structure may be characterized as an effective continuous mediumhaving (effective) anisotropic constitutive parameters

$\begin{matrix}{{ɛ_{x} = {ɛ_{y} = \frac{ɛ_{1} + {\eta \; ɛ_{2}}}{1 + \eta}}},} & (4) \\{{\frac{1}{ɛ_{z}} = {\frac{1}{1 + \eta}\left( {\frac{1}{ɛ_{1}} + \frac{\eta}{ɛ_{2}}} \right)}},} & (5) \\{{\mu_{x} = {\mu_{y} = \frac{\mu_{1} + {\eta\mu}_{2}}{1 + \eta}}},} & (6) \\{\frac{1}{\mu_{z}} = {\frac{1}{1 + \eta}\left( {\frac{1}{\mu_{1}} + \frac{\eta}{\mu_{2}}} \right)}} & (7)\end{matrix}$

where η=d₂/d₁ is the ratio of the two layer thicknesses, z is thedirection normal to the layers, and x, y are the directions parallel tothe layers. When the two materials comprising the interleaved structurehave electromagnetic parameters that are oppositely-signed, theconstitutive parameters (4)-(7) may correspond to an indefinite medium.For example, when the first material is a material having a permittivity∈₁<0 and the second material is a material having a permittivity ∈₂>0,the ratio η may be selected to provide an indefinite permittivity matrixaccording to equations (4)-(5) (moreover, for η substantially equal to|∈₁/∈₂|, the indefinite permittivity medium is substantially adegenerate indefinite permittivity medium). Alternately or additionally,when the first material is a material having a permeability μ₁<0 and thesecond material is a material having a permeability μ₂>0, the ratio ηmay be selected to provide an indefinite permeability matrix accordingto equations (6)-(7) (moreover, for η substantially equal to |μhd 1/μ₂|,the indefinite permeability medium is substantially a degenerateindefinite permeability medium).

Exemplary planar stacks of alternating materials, providing an effectivecontinuous medium having an indefinite permittivity matrix, include analternating silver/silica layered system described in B. Wood et al,“Directed subwavelength imaging using a layered medal-dielectricsystem,” Phys. Rev. B 74, 115116 (2006), and an alternatingdoped/undoped semiconductor layered system described in A. J. Hoffman,“Negative refraction in semiconductor metamaterials,” Nature Materials6, 946 (2007), each of which is herein incorporated by reference. Moregenerally, materials having a positive permittivity include but are notlimited to: semiconductors (e.g. at frequencies higher than a plasmafrequency of the semiconductor) and insulators such as dielectriccrystals (e.g. silicon oxide, aluminum oxide, calcium fluoride,magnesium fluoride), glasses, ceramics, and polymers (e.g. photoresist,PMMA). Generally these materials have a positive permeability as well(which may be substantially equal to unity if the material issubstantially nonmagnetic). In some embodiments a positive permittivitymaterial is a gain medium, which may be pumped, for example, to reduceor overcome other losses such as ohmic losses (cf. an exemplaryalternating silver/gain layered system described in S. Ramakrishna andJ. B. Pendry, “Removal of absorption and increase in resolution in anear-field lens via optical gain,” Phys. Rev. B 67, 201101(R) (2003),herein incorporated by reference). Examples of gain media includesemiconductor laser materials (e.g. GaN, AlGaAs), doped insulator lasermaterials (e.g. rare-earth doped crystals, glasses, or ceramics), andRaman gain materials. Materials having a negative permeability includebut are not limited to: ferrites, magnetic garnets or spinels,artificial ferrites, and other ferromagnetic or ferrimagnetic materials(e.g. at frequencies above a ferromagnetic or ferrimagnetic resonancefrequency of the material; cf. F. J. Rachford, “Tunable negativerefractive index composite,” U.S. patent application Ser. No.11/279/460, herein incorporated by reference). Materials having anegative permittivity include but are not limited to: metals (e.g. atfrequencies less than a plasma frequency of the metal) including thenoble metals (Cu, Au, Ag); semiconductors (e.g. at frequencies less thana plasma frequency of the semiconductor); and polar crystals (e.g. SiC,LiTaO₃, LiF, ZnSe) at frequencies within a resfrahlen band of the polarcrystal (cf. G. Schvets, “Photonic approach to making a material with anegative index of refraction,” Phys. Rev. B 67, 035109 (2003) and T.Tauber et al, “Near-field microscopy through a SiC superlens,” Science313, 1595 (2006), each of which is herein incorporated by reference).For applications involving semiconductors, the plasma frequency (whichmay be regarded as a frequency at which the semiconductor permittivitychanges sign) is related to the density of free carriers within thesemiconductor, and this free carrier density may be controlled invarious ways (e.g. by chemical doping, photodoping, temperature change,carrier injection, etc.). Thus, for example, a layered system comprisinginterleaved layers of a first semiconductor material having a firstplasma frequency and a second semiconductor material having a secondplasma frequency may provide an indefinite permittivity (per equations(4)-(5)) in a window of frequencies intermediate the first plasmafrequency and the second plasma frequency, and this window may becontrolled, e.g., by differently doping the first and secondsemiconductor materials.

In some applications a layered structure includes a succession ofadjacent layers that are substantially nonplanar. The precedingexemplary layered structure—consisting of successive planar layers, eachlayer having a layer normal direction (the z direction) that is constantalong the transverse extent of the layer and a layer thickness that isconstant along the transverse extent of the layer—may be extended to anonplanar layered structure, consisting of successive nonplanar layers,each layer having a layer normal direction that is non-constant alongthe transverse extent of the layer and, optionally, a layer thicknessthat is non-constant along the transverse extent of the layer. Someexamples of cylindrical and/or spherical layered structures aredescribed in A. Salandrino and N. Engheta, “Far-field subdiffractionoptical microscopy using metamaterial crystals: Theory and simulations,”Phys. Rev. B 74, 075103 (2006); Z. Jacob et al, “Optical hyperlens:Far-field imaging beyond the diffraction limit,” Opt. Exp. 14, 8247(2006); Z. Liu et al, “Far field optical hyperlens magnifyingsub-diffraction-limited objects,” Science 315, 1686 (2007); and H. Lee,“Development of optical hyperlens for imaging below the diffractionlimit,” Opt. Exp. 15, 15886 (2007); each of which is herein incorporatedby reference. More generally, for an alternating nonplanar layeredstructure, supposing that the layers have curvature radii substantiallyless than their respective thicknesses, and transverse layer thicknessgradients substantially less than one, the nonplanar layered structuremay be characterized as an effective continuous medium having(effective) anisotropic constitutive parameters as in equations (4)-(7),where the z direction is replaced by a layer normal direction that mayvary with position within the layered structure, the x direction isreplaced by a first transverse direction perpendicular to the layernormal direction, the y direction is replaced by a second transversedirection mutually perpendicular to the layer normal direction and thefirst transverse direction, and the layer thickness ratio η=d₂/d₁ is aratio of local layer thicknesses d₁ and d₂ that may vary with positionthroughout the layered structure (so the ratio η may vary with positionas well). The nonplanar layered structure may thus provide an indefinitemedium having a spatially-varying axial direction that corresponds tothe layer normal direction. Suppose, for example, that thespatially-varying axial direction of an indefinite medium is given by avector field u_(A)(r) that is equal to or parallel to a conservativevector field, i.e.

u_(A)∞∇Φ  (8)

for a scalar potential function Φ; then the indefinite medium may beprovided by a nonplanar layered structure where the interfaces ofadjacent layers correspond to equipotential surfaces of the function Φ.

With impedance-matching, a wave impedance of the output surface regionis substantially equal to a wave impedance of the adjacent medium. Thewave impedance of an isotropic medium is

$\begin{matrix}{Z_{0} = \sqrt{\frac{\mu}{ɛ}}} & (9)\end{matrix}$

while the wave impedance of a generally anisotropic medium is a tensorquantity, e.g. as defined in L. M. Barkovskii and G. N. Borzdov, “Theimpedance tensor for electromagnetic waves in anisotropic media,” J.Appl. Spect. 20, 836 (1974) (herein incorporated by reference). In someembodiments an impedance-matching is a substantial matching of everymatrix element of the wave impedance tensor (i.e. to provide asubstantially nonreflective interface for all incident polarizations);in other embodiments an impedance-matching is a substantial matching ofonly selected matrix elements of the wave impedance tensor (e.g. toprovide a substantially nonreflective interface for a selectedpolarization only). In some embodiments, the adjacent medium defines apermittivity ∈₁ and a permeability μ₁, where either or both parametersmay be substantially unity or substantially non-unity; the outputsurface region defines a permittivity ∈₂ and a permeability μ₂, whereeither or both parameters may be substantially unity or substantiallynon-unity; and the impedance-matching condition implies

$\begin{matrix}{\frac{ɛ_{2}}{ɛ_{1}} \cong \frac{\mu_{2}}{\mu_{1}}} & (10)\end{matrix}$

where ∈₂ and μ₂ may be tensor quantities. Defining a surface normaldirection and a surface parallel direction, some embodiments provide aoutput surface region that defines: a surface normal permittivity ∈₂^(⊥) corresponding to the surface normal direction and a surfaceparallel permittivity ∈₂ ^(□) corresponding to the surface paralleldirection; and/or a surface normal permeability μ₂ ^(⊥) corresponding tothe surface normal direction and a surface parallel permeability μ₂ ^(□)corresponding to the surface parallel direction; and theimpedance-matching condition may imply one or both of the followingconditions:

$\begin{matrix}{{\frac{ɛ_{2}^{\bot}}{ɛ_{1}} \cong \frac{ɛ_{1}}{ɛ_{2}^{\bullet}}},{\frac{\mu_{2}^{\bot}}{\mu_{1}} \cong {\frac{\mu_{1}}{\mu_{2}^{\bullet}}.}}} & (11)\end{matrix}$

Where the output surface region is a curved surface region, the surfacenormal direction and the surface parallel direction can vary withposition along the input surface region.

Nonplanar layered structures may be fabricated by various methods thatare known to those of skill in the art. In a first example, J. A. Folta,“Dynamic mask for producing uniform or graded-thickness thin films,”U.S. Pat. No. 7,062,348 (herein incorporated by reference), describesvapor deposition systems that utilize a moving mask, where the velocityand position of the moving mask may be computer controlled to preciselytailor the thickness distributions of deposited films. In a secondexample, Tzu-Yu Wang, “Graded thickness optical element and method ofmanufacture therefor,” U.S. Pat. No. 6,606,199 (herein incorporated byreference), describes methods for depositing graded thickness layersthrough apertures in a masking layer.

While many exemplary metamaterials are described as including discreteelements, some implementations of metamaterials may include non-discreteelements or structures. For example, a metamaterial may include elementscomprised of sub-elements, where the sub-elements are discretestructures (such as split-ring resonators, etc.), or the metamaterialmay include elements that are inclusions, exclusions, layers, or othervariations along some continuous structure (e.g. etchings on asubstrate). Some examples of layered metamaterials include: a structureconsisting of alternating doped/intrinsic semiconductor layers (cf. A.J. Hoffman, “Negative refraction in semiconductor metamaterials,” NatureMaterials 6, 946 (2007), herein incorporated by reference), and astructure consisting of alternating metal/dielectric layers (cf. A.Salandrino and N. Engheta, “Far-field subdiffraction optical microscopyusing metamaterial crystals: Theory and simulations,” Phys. Rev. B 74,075103 (2006); and Z. Jacob et al, “Optical hyperlens: Far-field imagingbeyond the diffraction limit,” Opt. Exp. 14, 8247 (2006); each of whichis herein incorporated by reference). The metamaterial may includeextended structures having distributed electromagnetic responses (suchas distributed inductive responses, distributed capacitive responses,and distributed inductive-capacitive responses). Examples includestructures consisting of loaded and/or interconnected transmission lines(such as microstrips and striplines), artificial ground plane structures(such as artificial perfect magnetic conductor (PMC) surfaces andelectromagnetic band gap (EGB) surfaces), and interconnected/extendednanostructures (nano-fishnets, elongated SRR woodpiles, etc.).

The term “metamaterials” as used herein may be understood to include“electromagnetic crystals” (e.g., photonic crystals, electromagneticband gap structures (EBG), and/or photonic bandgap structures (PBG)).Electromagnetic crystals are periodic structures composed of dielectricor metallic regular lattices with a given unit cell. The periodicstructures function is to affect the propagation of electromagneticwaves. A periodic structures (e.g., a dielectric or metallo-dielectricnanostructure) may affect the propagation of electromagnetic waves inthe same way as the periodic potential in a semiconductor crystalaffects the electron motion by defining allowed and forbidden electronicenergy bands. Photons (behaving as waves) propagate through thisstructure—or not—depending on their wavelength. Wavelengths of lightthat are allowed to travel are known as modes, and groups of allowedmodes form bands. Disallowed bands of wavelengths are called photonicband gaps. See e.g., J. D. Joannopoulos et al, Photonic Crystals:Molding the Flow of Light, 2^(nd) Edition, Princeton Univ. Press, 2008.

FIG. 1 shows an exemplary apparatus 100 which is configured to modify anincident free space electromagnetic wave. Apparatus 100 includes amaterial (e.g., material block 110 made of artificially structuredmaterial) configured to intercept and modify an incident free spaceelectromagnetic wave. The material may have an adjustable spatialdistribution of electromagnetic properties or parameters (e.g.,dielectric constant ∈, permeability μ, impedance η, conductivity σ,refractive index n, etc.). The electromagnetic properties or parametersof the material may have selected values that define particular changesor modifications made to the incident electromagnetic wave by thematerial. For example, FIG. 1 shows a spatial distribution of anelectromagnetic parameter (e.g., refractive index n) which has astep-like feature 120 that may act to partially reflect the incidentelectromagnetic wave.

The material may for example, include one or more of a photonic bandgapmaterial, a metamaterial, a broadband metamaterial. Further, thematerial may, for example, be transmissive material having a variablerefractive index. Alternatively or additionally, the material may, forexample, include at least one layer switchable between a transmissivestate and a reflective state. The transmissive and/or reflective statesmay be only partially so. The material may be switchable states inresponse to an applied control signal (e.g., an electric field, anelectric current, a magnetic field, an ultrasonic signal, mechanicalstress or strain, an electromagnetic signal, and/or a light wave). Forexample, the material may, be an optically-switched metamaterial, andthe control signal an optical signal of having a defined wavelengthand/or intensity.

Material block 110 may include an arrangement of discrete elements,which provide the adjustable spatial distribution of electromagneticparameters. The discrete elements may, for example, include one or moreman-made metamaterial elements (e.g., resonant structures).

Material block 110 may present varying amounts of optical path length ordelay to incident electromagnetic waves. The amount or quantity of theoptical path length may be a function of the spatial distribution ofelectromagnetic parameters in block 110. FIG. 12A shows optical pathlengths A of transmitted electromagnetic waves in transmissive materialblock 110 for various exemplary refractive index profiles. Inparticular, FIG. 12A shows three exemplary cases (Cases I-III) ofrefractive indices profiles in the material block having an overallthickness L. Cases I-III correspond to bi-layer refractive indexprofiles having a refractive index value (n_(i)) over each layerthickness (s_(i)). In Case I, material block 110 has the same refractiveindex (n1) throughout its thickness L. Thus, a step difference in therefractive index at location 120 is trivially zero. The optical pathlength Λ of an electromagnetic wave transmitted through material block110 is proportional to L*n1. In Case II, material block 110 has arefractive index n2 over a distance s₂=a and a refractive index n1 overa distance s₁=b. Thus, a step difference in the refractive index atlocation 120 is (n2−n1). The optical path length Λ of a transmittedelectromagnetic wave in material block 110 is equal to a*(n2−n1)+L*n1.In Case III, material block 110 has a refractive index (−n1) over adistance s₂=a and a refractive index n1 over a distance s₁=b with aresulting optical path length Λ equal to (b−a)*n1. When distancea=distance b, then the optical path length Λ reduces to zero. Whendistance a is greater than distance b, then the optical path length Λ isnegative.

Thus, material block 110, which has a controllable refractive indexprofile, may operate as a variable path delay element. The material maybe controlled (e.g., according to rules of transformation optics) sothat the material presents a propagation distance (e.g., optical pathlength Λ) that may be larger than or less than the physical dimension ofmaterial block 110 (e.g., thickness L).

Material block 110 with an adjustable spatial distribution ofelectromagnetic parameters operating as a transmissive variable pathdelay element may have one or more states that are at least partiallyreflective. FIG. 12B shows, for example, a variable delay element withthree states (e.g., Cases I-III) corresponding to different refractiveindex profiles. The figure shows changes in the intensity of anelectromagnetic wave reflected by a step (e.g., step 120) in therefractive index profile of block 110. Case 1 in which a refractiveindex step at location 120 is nominally zero corresponds to atransmissive state with no reflection (R=0). Case 2 having a finiterefractive index step (n2−n1) at location 120 corresponds to a partiallyreflective state with a reflection coefficient R=((n2−n1)/(n1+n2))**2.Case 3 having a multilayered refractive index profile (e.g., a stepup-step down profile) corresponds to a partially reflective state inwhich constructive or destructive interference of the reflected wavesfrom the up and down steps in the profile may lead to a reflectioncoefficient R, which is larger or smaller than the reflectioncoefficient R in Case 2.

Further, material block 110 with an adjustable spatial distribution ofelectromagnetic parameters operating as a variable path delay elementsmay have one or more states that are at fully reflective (e.g., bysubstantially completely blocking transmission). FIG. 12C shows, forexample, a block 110 made of photon crystal material. An incidentelectromagnetic wave may be transmitted or fully reflected by block 110depending on whether the photonic crystal is in a transmissive orreflective state, respectively.

Changing the optical path length traversed by an electromagneticeffectively phase modulates the electromagnetic wave. Dynamicallyvarying the spatial distribution of electromagnetic parameters inmaterial block 110 in may allow time-dependent phase shifts to beintroduced in the electromagnetic waves. FIG. 12D shows an example of atime-dependent phase modulation of a carrier electromagnetic waveaccording to a modulation function m(t). The phase modulation achievedmay be suitably converted into amplitude modulation. FIG. 12E shows, forexample, an incident electromagnetic wave 1210 incident on a surface ofmaterial block 110 in which the position of a step 1250 in the spatialprofile of at least one electromagnetic parameter is dynamicallychanged. At least a portion of the incident wave may be reflected by thesurface (e.g., reflected wave 1220). The movement of step 1250 maygenerate a phase modulated reflected wave 1230. Superposition of thisphase modulated wave 1230 with reflected wave 1220 may result in anamplitude modulated wave 1240.

With renewed reference to FIG. 1, apparatus 100 further includes acontroller 130, which may be configured to dynamically adjust theposition, size and/or shape of the spatial distribution ofelectromagnetic parameters in the material, for example, by applyingsuitable control signals to the material. The control signals maydynamically adjust the properties or operation of thediscreet/metamaterial elements in the material to obtain a selectedspatial distribution of the electromagnetic parameters. Thus, theelectromagnetic parameters in the material may be a function of bothposition and time (e.g., ∈(x, y, z, t), μ(x, y, z, t), η(x, y, z, t),σ(x, y, z, t), n(x, y, z, t), etc.). Controller 130 may modify theelectromagnetic parameters in the material according to a modulationsignal or function (e.g., m (t)).

Apparatus 100 may also include a sensor circuit (e.g., sensor 140) tosense properties of the incident electromagnetic wave (e.g. frequency,rate of change of frequency, bandwidth etc.) and to relay suchinformation to controller 130.

Controller 130 may, for example, be configured to adjust the spatialdistribution (e.g., by changing the position of step-like feature 120)to introduce a time-varying path delay d (t) in the modifiedelectromagnetic wave relative to the incident electromagnetic wave. Theintroduced time-varying path delay d (t) may, for example, asubstantially pseudo-random or random function of time, or asubstantially periodic function of time. The time-varying path delayd(t) may be a substantially continuous function of time over a timeinterval substantially larger than a cycle (1/f) of the incidentelectromagnetic wave. The function may have first or second orderdiscontinuities, which may define the intervening time interval overwhich it is continuous. Exemplary time-varying path delay d (t)functions are linear (e.g., d(t)≈αt+β₀) or quadratic (e.g.,d(t)≈αt²+βt+γ₀) in time. A linearly varying path delay may result in amodified electromagnetic wave that is shifted in frequency by a fixedamount from the incident wave. A quadratically varying path delay maylikewise result in a modified electromagnetic wave that is shifted infrequency from the incident wave, but by an amount that is time varying.(See e.g., FIG. 13).

FIG. 13 shows, for example, a triangle wave or linear sawtooth-shapedmodulation signal m(t), which is a first order discontinuous function.Changing the path delay of an electromagnetic wave (frequency f₀)according to this modulation function m(t) may result in a modifiedelectromagnetic wave that is shifted in frequency by a fixed amount (≈α)from the incident wave. In this case, there may be little or minimalenergy shift to other frequencies (i.e. other than f₀+α). FIG. 13 alsoshows, for example, a quadratic sawtooth-shaped modulation signal m(t),which is second order discontinuous (i.e. with abrupt changes in slope).Changing the path delay of an electromagnetic wave (frequency f₀)according to this modulation function m(t) may result in a modifiedelectromagnetic wave that is shifted in frequency by a linearly varyingamount or chirp (e.g., ≈αt) from the incident wave. In both the casesshown in FIG. 13, the frequency shift is proportional to the incidentfrequency (i.e., a Doppler-like frequency shift) and to the component ofthe path delay change parallel to the propagation direction.

With renewed reference to FIG. 1 and the operation of controller 130,the time-varying phase shift φ(t) may be a selected function such thatmaterial block 110 has an apparent velocity (≈dφ(t)/dt) and/or anapparent acceleration (≈d²φ(t)/d²t) that are different than its actualvelocity and/or acceleration, respectively. In the case of a linearlyvarying path delay d(t) (e.g., d(t)≈αt+β₀), a frequency f of themodified electromagnetic wave may be shifted relative to a frequency fof the incident electromagnetic wave by an amount δf(≈α/2π).

Controller 130 may be configured to dynamically vary an effectiveposition of the selected spatial profile to time-modulate a property ofthe modified electromagnetic wave. The change in the effective positionof the selected spatial profile may include one or more of atranslation, a rotation, a tilt, a curvature change, a size and/or shapechange of the selected spatial profile.

In an exemplary implementation of apparatus 100, controller 130 may beconfigured to dynamically change an effective position of the selectedspatial profile to time-modulate a phase of the modified electromagneticwave, for example, in response to an external signal. In such animplementation, apparatus 100 may operate or act as a variable opticalelement or delay. Controller 130 may be configured to dynamically varythe effective position continuously in space. For example, step-likefeature 120 may be varied substantially continuously in space betweenend positions A and B (FIG. 2) in a substantially cyclical oroscillatory fashion.

The extent or range of the variation in the effective position may beselected with consideration of the characteristics of the incidentand/or modified electromagnetic waves. For example, controller 130 maybe configured to vary the effective position of the selected spatialprofile over a distance that is a fraction of, comparable to, or largerthan a wavelength of the incident electromagnetic wave in the material.For example, controller 130 may be configured to vary the effectiveposition of the selected spatial profile in distance increments smallerthan about 0.03 of a wavelength of the incident electromagnetic wave inthe material so that a reflected wavefront changes smoothly. Thesedistance increments may equivalently correspond to controlling the phaseof the modified electromagnetic wave with an accuracy substantiallybetter than about 0.06*π radians.

In alternative implementations or operations of apparatus 100,controller 130 may be configured to vary the effective position of theselected spatial profile in distance increments equal to or larger than0.03 of a wavelength of the incident electromagnetic wave in thematerial. These distance increments may equivalently correspond tocontrolling the phase of the modified electromagnetic wave with anaccuracy of about 0.06*π radians. In other implementations or operationsof apparatus 100, controller 130 may be configured to vary the effectiveposition of the selected spatial profile in distance increments equal toor larger than about 0.25 of a wavelength of the incidentelectromagnetic wave in the material. These distance increments mayequivalently correspond to controlling the phase of the modifiedelectromagnetic wave with an accuracy of about an accuracy of about0.5*πradians.

FIGS. 14A and 14B show exemplary representations of the “frequencyshifting” phenomena that may be obtained with moving objects. FIG. 14Ashow a vehicle moving relative to a conventional Doppler radararrangement with a relative velocity V_(rel). The radar emits anelectromagnetic wave having a frequency f₀ toward the moving vehicle.The movement of the vehicle results in detection by the Doppler radar ofa reflected wave, whose frequency is “Doppler” shifted by an amountΔf≈2V_(rel)*f₀/c. FIG. 14B shows a similar Doppler shifting effectcaused by an oscillating mirror, which reflects an electromagnetic waveincident by the Doppler radar. The shift in frequency in this case maybe Δf≈2V_(effective)*f₀/c, where V_(effective) is the velocity of theoscillating mirror with respect to the Doppler radar.

With renewed reference to FIG. 1, controller 130 may be configured todynamically change the effective position of the selected spatialprofile at a rate substantially different that an actual velocity v ofthe material. In exemplary implementations of apparatus 100, controller130 may be configured to change the effective position of the selectedspatial profile cyclically with a cycle frequency about equal to orgreater than a modulation frequency of the incident electromagneticwave.

In other exemplary implementations of apparatus 100, the effectiveposition of the selected spatial profile may be changed such that aportion of the energy of the modified electromagnetic wave has afrequency translated outside a pre-defined frequency band of a receiverof the modified electromagnetic wave. (See e.g., FIG. 14B). Controller130 may vary the effective position of the selected spatial profile sothat a portion of the energy of the modified electromagnetic wave isshifted in frequency by a fixed amount relative to the incidentelectromagnetic wave. (i.e. the modified electromagnetic waveapproximates a wave reflected from a surface moving continuously atvelocity v). Alternatively or additionally, in cases where the where theincident electromagnetic wave has a frequency bandwidth, controller 130may be configured to dynamically change the effective position of theselected spatial profile so that a portion of the energy of the modifiedelectromagnetic wave has a frequency translated outside the frequencybandwidth of the incident electromagnetic wave. Controller 130 may varythe effective position of the selected spatial profile so that a portionof the energy of the modified electromagnetic wave is shifted infrequency by a fixed amount (e.g., Δf≈v/c) relative to the incidentelectromagnetic wave so that the modified electromagnetic waveapproximates a wave reflected from a surface moving continuously at avelocity≈v.

Controller 130 may be configured to dynamically change the effectiveposition of the selected spatial profile according to a random orpseudo-random pattern such that any temporal phase coherence in themodified electromagnetic wave is reduced or eliminated. Alternatively oradditionally, controller 130 may be configured to dynamically change theeffective position of the selected spatial profile at a rate sufficientto substantially reduce a temporal phase correlation of the incident andthe modified electromagnetic waves. Controller 130 may be configured todynamically change the effective position of the selected spatialprofile according to a pattern having selected amplitude and frequencycomponents so that for at least one incident electromagnetic wavefrequency the modified electromagnetic wave is substantiallyphase-continuous or jumps in phase by full wavelengths

Controller 130 may be configured to vary the effective position of theselected spatial profile according to a linear repeating pattern (e.g.,a saw tooth shaped profile). In cases where the incident electromagneticwave has a time-varying frequency [a chirp] controller 130 may beconfigured to dynamically vary the effective position of the selectedspatial profile with a substantially different chirp rate than theincident electromagnetic wave. Controller 130 may use frequencyinformation sensed by sensor 140 or received from other sources to dodetermine the rate at which the effective position should be changed.

The spatial profile of the at least one electromagnetic parameter in thematerial may be selected to act as a reflector of the incidentelectromagnetic wave. The selected profile may provide partialreflections so that the modified electromagnetic wave is effectively asum of reflections from a first surface and a second surface. (See e.g.,FIG. 12C). Further, controller 130 may be configured to dynamically varya property (e.g., position, shape or strength) of the selected spatialprofile to vary reflectivity or impedance so that a ratio of theamplitudes of the reflections from the first and second surface istime-dependent. FIG. 15 shows for example, a material block 110 in whichthe spatial profile of the at least one electromagnetic parameter (e.g.,refractive index) is dynamically varied to present reflective steps(e.g., Step 1 and Step 2) having time-varying amplitudes. In particular,the figure shows Step 1 decreasing from its maximum value to zero andconversely Step 2 increasing from zero to its maximum value, over afinite time interval. Accordingly, the ratio of the amplitudes of thewaves (1 and 2) that are reflected by steps 1 and 2 may change as afunction to the relative heights of the two steps.

It will be understood that while FIG. 1 shows an exemplary a rectangularstep-like feature 120 in the spatial distribution of an electromagneticparameter, various implementations of apparatus 100 may include anysuitable selected spatial profile of at least one electromagneticparameter in the material. The selected spatial profile may, forexample, have a pulse-like shape. Alternatively, the selected spatialprofile may be a sequence of spatial steps arranged to act as a Braggdiffraction grating.

In three dimensions, the selected spatial profile may present a planarsurface to the incident electromagnetic wave or a curved surface, whichmay focus or defocus the incident electromagnetic wave. When theselected spatial profile is interior to the material it may define anoutward material layer extending from a spatial feature in the profileto an exterior surface of the material (FIG. 1). Controller 130 may beconfigured to adjust the spatial distribution of electromagneticparameters in the material so that the outward material layer has adesired interfacial property. Controller 130 may, for example, adjustthe spatial distribution so that an electromagnetic impedance η of theoutward material layer matches that of a medium across the externalsurface of the material and/or provides a reflection-free externalsurface.

In exemplary implementations of apparatus 100, the material in block 110may include materials which exhibit a negative index of refraction underselect conditions. Such an apparatus 100 may be configured so that thenegative index of refraction characteristics give rise to phase reversalin the modification of the incident electromagnetic wave.

In an exemplary implementation, apparatus 100 may be configured to actas a passive transponder. (See e.g., FIG. 16A).

In further exemplary implementations, apparatus 100 may be configured toredirect the incident electromagnetic wave in a specified direction.FIG. 16 B shows, for example, apparatus 100 configured to operate as afocusing device. Controller 130 may be used to modify the spatialprofile of the at least one electromagnetic parameter in the materialblock 110 to present a suitable surface (e.g., curved surface 1610) forfocusing the incident electromagnetic waves toward a focal point.

In an exemplary implementation apparatus 100 may, for example, includesuitable retro reflector structures (e.g., corner cube structures)disposed in the material to redirect the incident electromagnetic wavein the specified direction. FIG. 16C shows, for example, apparatus 100having an attached corner cube mirror surface 1620. Surface 1620 may besuitably disposed relative to block 110 so that electromagnetic wavesincident on block 110 are retro reflected of surface 1620. block 110 toincident electromagnetic waves are retro reflected. Alternatively,material block 110 itself may be configured to act as a retroreflector,for example, by selection of a suitable spatial profile of the at leastone electromagnetic parameter therein. FIG. 16D shows an exemplaryretro-reflective profile 1630, which may be dynamically generated bycontroller 130 in material block 110.

Apparatus 100 may also include an electromagnetic radiation detector 150coupled to block 110 and controller 130. Such an apparatus 100 may beconfigured to operate as a demodulator and/or signal correlator.

In general, controller 130 may be configured to modulate an amplitude, adirection, a phase, and/or a frequency of the incident electromagneticwave according to an information carrying signal. In an exemplaryimplementation of apparatus 100, a source 160 of the incidentelectromagnetic wave may be coupled to block 110 so that apparatus 100can operate as a signal transmitter. FIG. 16E shows an exemplaryconfiguration of apparatus 100 configured to operate as a signaltransmitter. An external source provides electromagnetic radiation,which is modulated according to a signal m(t) applied to controller 13.The modulate signal is transmitted to a receiver. Conversely, FIG. 16Fshows an exemplary configuration of apparatus 100 configured to operateas a signal receiver/demodulator. A variable path delay introduced byblock 110 may result in a frequency shift so that the receiver canoperate at a different frequency than the transmitter frequency, forexample, to avoid interference. Alternatively, block 110 may operate todemodulate or correlate the phase modulation present on the transmittedsignal.

FIG. 3 shows an exemplary apparatus 300, which is configured to act as avariable reflector. Apparatus 300 includes two or more layers ofreflective material (e.g., layers 310 a and 310 b), at least one layerbeing made or controllable metamaterial elements (e.g., elements 300 a).Apparatus 300 may also include a controller 330 (e.g., controller 130)which applies suitable control signals to the controllable layers tovary the position of an effective reflective surface (e.g., surface310). Like apparatus 100, apparatus 300 may operate as a passivetransponder.

An exemplary version of apparatus 300 includes a stack of one or morelayers (e.g., layers 310 a and 310 b) having controllable reflectiveproperties provided by metamaterial elements (e.g., elements 300 a)therein. Controller 330 may be configured to adjust the controllablereflective properties of at least one layer by applying one or more ofan electric field, an electric current, a magnetic field,electromagnetic energy, light, heat, mechanical stress or strain,acoustic and/or ultrasound energy to the at least one layer. Inoperation, controller 330 may be dynamically adjust the controllablereflective properties of the one or more layers to present an effectivereflective surface at varying positions (e.g., position 310 and 310′) ororientations in the stack as a function of time. The variations inposition or orientation of the effective reflective surface mayintroduce a time-varying path delay d (t) in a reflected electromagneticwave relative to the incident electromagnetic wave.

As in apparatus 100, controller 330 in apparatus 300 may be configuredso that the introduced time-varying path delay d (t) is, for example, asubstantially pseudo-random or random function of time, or asubstantially periodic function of time. The time-varying path delayd(t) may be a substantially continuous function of time over a timeinterval substantially larger than a cycle (1/f) of the incidentelectromagnetic wave. The function may have first or second orderdiscontinuities, which may define the intervening time interval overwhich it is continuous. Exemplary time-varying path delay d (t)functions are linear (e.g., d(t)≈αt+β₀) or quadratic (e.g.,d(t)≈αt²+βt+γ₀) in time.

The time-varying phase shift φ(t) may be a selected function such thatthe stack of one or more layers has an apparent velocity (≈dφ(t)/dt)and/or an apparent acceleration (≈d²φ(t)/d²t) that are different than anactual velocity and/or acceleration, respectively. In the case of alinearly varying path delay d (t) (e.g., d(t)≈αt+β₀), a frequency f′ ofthe modified electromagnetic wave may be shifted relative to a frequencyf of the incident electromagnetic wave by an amount δf(≈α/2π).

The stack of one or more layers with controllable reflective propertiesmay constitute a volume of a material that has a change in state thatmoves through it in response to a spatially varying signal applied bycontroller 330.

Controller 330 may be configured to dynamically change an effectiveposition of the reflective surface (e.g., surface 310) to time-modulateproperties (e.g., the phase) of the reflected electromagnetic wave.Controller 330 may adjust the controllable reflective properties of atleast one layer in response to an external signal and/or externalcommand so that apparatus 300 operates as an variable optical element ordelay. The external signal may, for example, be an information carryingsignal, and controller 330 may be is configured to adjust thecontrollable reflective properties so that the reflected electromagneticwave is modulated in direction, amplitude, phase and/or or frequencyaccording to the information carrying signal.

Each layer with controllable reflective properties in the stack may havea plurality of states including at least a reflective state, atransmissive state and/or a variable index state. The reflective stateand transmissive states may be only partially so. Further, the pluralityof states of a layer may include a state in which at least a portion ofthe layer has a negative index of refraction under select conditions.

Controller 330 may be configured to switch a layer with controllablereflective properties between its states.

With renewed reference to FIG. 3, at least one of the layers withcontrollable reflective properties in apparatus 300 has a substantiallyuniform thickness. This feature may allow a reflected wavefront shape toremain unchanged. At least one of the layers may have a thickness ofless than about 0.03 of a wavelength of the incident electromagneticwave in the stack. Such a layer thickness may correspond to a change inphase of the modified electromagnetic wave of less than about0.06*πradians. Alternatively or additionally, at least one of the layerswith controllable reflective properties may have a thickness equal to orlarger than about 0.03 of a wavelength of the incident electromagneticwave in the stack. Such a layer thickness may correspond to a change inphase of the modified electromagnetic wave of about 0.06*π radians.Further, at least one of the layers with controllable reflectiveproperties may have a thickness equal to or larger than 0.25 of awavelength of the incident electromagnetic wave. Such a layer thicknessmay correspond to a change in phase of the modified electromagnetic waveof about 0.5*π radians.

Alternatively or additionally, at least one of the layers (e.g., layer310 c, FIG. 4) with controllable reflective properties may have asubstantially varying thickness in a transverse direction. The thicknessmay, for example, vary substantially linearly along a transverse axis.Such a layer may operate as a variable prism on the incidentelectromagnetic wave. Alternatively, the thickness may varysubstantially quadratically along a transverse axis. Such a layer mayoperate as a variable lens. In general, one or more of the layers withcontrollable reflective properties may have a substantially concaveand/or convex shape. Layers with substantially uniform thickness may beplanar or may have a curved shape. The different shapes of the layersmay be selected with in consideration of a desired shape of thereflective surface (e.g., surface 310) to be presented to the incidentelectromagnetic wave.

Like in apparatus 100, controller 330 in apparatus 300 may be configuredto modulate an amplitude, a direction, a phase, and/or a frequency ofthe incident electromagnetic wave according to an information carryingsignal. Like apparatus 100, apparatus 300 may also include anelectromagnetic radiation detector 150. Such an apparatus 300 may beconfigured to operate as a demodulator and/or signal correlator.Similarly like apparatus 100, apparatus 300 may include a source 160 ofthe incident electromagnetic wave so that apparatus 300 can operate as asignal transmitter.

In exemplary implementations of apparatus 300, controller 330 may beconfigured to dynamically change the effective position of thereflective surface at a rate substantially different that an actualvelocity v of the stack. Controller 330 may, for example, vary aneffective position of the reflecting surface so that a reflectedelectromagnetic wave is shifted in frequency by a fixed amount tosimulate reflection, for example, from a continuously moving surface.Controller 330 may be configured to change the effective position of thereflective surface cyclically with a cycle frequency about equal to orgreater than a modulation frequency of the incident electromagneticwave. The effective position of the reflective surface may bedynamically changed so that a portion of energy of the reflectedelectromagnetic wave has a frequency translated outside a pre-definedfrequency band of a receiver of the modified electromagnetic wave.Additionally of alternatively, a portion of the energy of the reflectedelectromagnetic wave may have a frequency translated outside thefrequency band width of the incident electromagnetic wave.

Controller 330 may be configured to change the effective position of thereflective surface in apparatus 300 at a rate sufficient tosubstantially reduce a temporal phase correlation of the incident andthe reflected electromagnetic waves. For example, controller 330 mayvary the effective position of the reflective surface according to arandom or pseudo-random pattern such that any temporal phase coherencein the reflected radiation is reduced or eliminated. In instances wherethe incident electromagnetic wave has a time-varying frequency [achirp], controller 330 may be configured to dynamically vary theeffective position of the reflective surface with a chirp ratesubstantially different than that of the incident electromagnetic wave.

Controller 330 may be configured to vary an effective position of thereflective surface in a repeating pattern (e.g., in a linear saw toothpattern). The repeating pattern may be selected to have particularamplitude and frequency components so that for at least one incidentelectromagnetic wave frequency, the reflected electromagnetic wave issubstantially phase-continuous. The effective position of the reflectivesurface may be varied so that the reflected electromagnetic wave iseffectively a sum of reflections from a first surface and a secondsurface. Further, controller 330 may vary the effective position of thereflective surface so that a relative amplitude of the reflections fromthe first and second surface is time-dependent (e.g., such that the“new” reflecting surface can “fade in” over the old one, rather thanjumping abruptly).

In general, apparatus 300 may be configured to redirect the incidentelectromagnetic wave in a specified direction. Apparatus 300 may includea retro reflector. The retro reflector may, for example, include cornercube structures disposed in the stack of one or more layers.Alternatively or additionally, the one or more layers with controllablereflective properties may themselves be configured to act as aretroreflector.

In apparatus 300, the one or more layers with controllable reflectiveproperties may include a photonic bandgap material, a metamaterial,and/or a broadband metamaterial (e.g., optically-switched metamaterialelements, electrically and/or electro-magnetically-switched metamaterialelements). The one or more layers may include one or more materials thatexhibit a negative index refraction at least under select conditions.Controller 330 may be configured to apply an optical signal having adefined wavelength and/or intensity, an electrical and/or anelectro-magnetic signal as appropriate to the metamaterial elements toswitch one or more of the layers between reflective and transmissivestates.

FIG. 5 shows an exemplary apparatus 500, which is configured to act as avariable phase or time delay. Apparatus 500 includes two or more layersof transmissive material (e.g., layers 510 a and 510 b) havingcontrollable indices of refraction. At least one layer may be made ofcontrollable metamaterial elements (e.g., elements 500 a). Apparatus 500includes a controller 530 (e.g., controller 130 or controller 330) whichapplies suitable control signals to one or more of the controllablelayers to vary their indices of refraction. Like apparatuses 100 and300, apparatus 500 may operate as a passive transponder.

An exemplary version of apparatus 500 includes a stack of one or morelayers (e.g., layers 510 a and 510 b) having controllable transmissiveproperties (e.g., controllable indices of refraction) provided bymetamaterial elements (e.g., elements 500 a) therein. Controller 530 maybe configured to dynamically adjust the controllable indices ofrefraction of the one or more layers to at least partially transmit anincident electromagnetic wave having a frequency f, and to introduce atime-varying path delay d (t) in a transmitted electromagnetic waverelative to the incident electromagnetic wave to introduce atime-varying path delay d (t) in a reflected electromagnetic waverelative to an incident electromagnetic wave. Controller 530 may adjustthe indices of refraction of at least one layer by applying one or moreof an electric field, an electric current, a magnetic field,electromagnetic energy, light, heat, mechanical stress or strain,acoustic and/or ultrasound energy to the at least one layer.

Controller 530 in apparatus 500 may be configured so that the introducedtime-varying path delay d (t) is, for example, a substantiallypseudo-random or random function of time, or a substantially periodicfunction of time. The time-varying path delay d(t) may be asubstantially continuous function of time over a time intervalsubstantially larger than a cycle (1/f) of the incident electromagneticwave. The function may have first or second order discontinuities, whichmay define the intervening time interval over which it is continuous.Exemplary time-varying path delay d (t) functions are linear (e.g.,d(t)≈αt+β₀) or quadratic (e.g., d(t)≈αt²+βt+γ₀) in time.

The time-varying phase shift φ(t) may be a selected function such thatthe material has an apparent velocity (≈dφ(t)/dt) and/or an apparentacceleration (≈d²φ(t)/d²t) that are different than its actual velocityand/or acceleration, respectively. In the case of a linearly varyingpath delay d (t) (e.g., d(t)≈αt+β₀), a frequency f of the modifiedelectromagnetic wave may be shifted relative to a frequency f of theincident electromagnetic wave by an amount δf (≈α/2π).

The one or more layers with controllable indices of refraction mayconstitute a volume of a material that has a change in state that movesthrough it in response to a spatially varying signal applied bycontroller 530.

Controller 530 may be configured to dynamically change the controllableindices of refraction to time-modulate properties (e.g., the phase) ofthe transmitted electromagnetic wave. Controller 530 may adjust thecontrollable indices of refraction of at least one layer in response toan external signal and/or external command so that apparatus 500operates as an variable phase or time delay. The external signal may,for example, be an information carrying signal, and controller 530 maybe is configured to adjust the controllable indices of refraction sothat the transmitted electromagnetic wave is modulated in direction,amplitude, phase and/or or frequency according to the informationcarrying signal.

Each layer with controllable indices of refraction may have a pluralityof states including at least a reflective state, a transmissive stateand/or a variable index state. The reflective state and transmissivestates may be only partially so. Controller 530 may be configured toswitch a layer with controllable indices of refraction between itsstates. Further, the plurality of states of a layer may include a statein which at least a portion of the layer has a negative index ofrefraction under select conditions.

With renewed reference to FIG. 5, at least one of the layers withcontrollable indices of refraction in apparatus 530 may have asubstantially uniform thickness. This feature may, for example, allow atransmitted wavefront shape to remain unchanged. At least one of thelayers may have a thickness of less than about 0.03 of a wavelength ofthe incident electromagnetic wave in the stack. Such a layer thicknessmay correspond to a change in phase of the modified electromagnetic waveof less than about 0.06*π radians. Alternatively or additionally, atleast one of the layers with controllable indices of refraction may havea thickness equal to or larger than about 0.03 of a wavelength of theincident electromagnetic wave in the stack. Such a layer thickness maycorrespond to a change in phase of the modified electromagnetic wave ofabout 0.06*π radians. Further, at least one of the layers withcontrollable indices of refraction may have a thickness equal to orlarger than 0.25 of a wavelength of the incident electromagnetic wave.Such a layer thickness may correspond to a change in phase of themodified electromagnetic wave of about 0.5*π radians.

Alternatively or additionally, at least one of the layers withcontrollable indices of refraction may have a substantially varyingthickness in a transverse direction. The thickness may, for example,vary substantially linearly along a transverse axis. Such a layer mayoperate as a variable prism on the incident electromagnetic wave.Alternatively, the thickness may vary substantially quadratically alonga transverse axis. Such a layer may operate as a variable lens. Ingeneral, one or more of the layers with controllable indices ofrefraction may have a substantially concave and/or convex shape. Layerswith substantially uniform thickness may be planar or may have a curvedshape. The different shapes of the layers may be selected with inconsideration of a desired shape of the modified wavefront surface withrespect to that of the incident electromagnetic wave.

In exemplary implementations of apparatus 500, a first of pair of layersmay have a thickness that varies substantially linearly along a firsttransverse axis and a second of the pair of layers may have a thicknessthat varies substantially linearly along a second transverse axis. Thefirst of pair of layers may have a thickness that increases along thetransverse axis and he second of the pair of layers may have a thicknessthat decreases along the transverse axis. In a further exemplaryimplementation of apparatus 500, at least one of the layers havingcontrollable indices of refraction may have a thickness profilecorresponding to a Zernike polynomial (or other polynomial of anorthogonal set of polynomials). Such a thickness profile may compensatefor optical aberrations in the modified electromagnetic wave.

Like in apparatuses 100 and 300, controller 530 in apparatus 500 may beconfigured to modulate an amplitude, a direction, a phase, and/or afrequency of the incident electromagnetic wave according to aninformation carrying signal. Like apparatus 100, apparatus 500 may alsoinclude an electromagnetic radiation detector 150. Such an apparatus 500may be configured to operate as a demodulator and/or signal correlator.Similarly like apparatus 100, apparatus 500 may include a source 160 ofthe incident electromagnetic wave so that apparatus 500 can operate as asignal transmitter.

In exemplary implementations of apparatus 500, controller 530 may beconfigured to dynamically change the indices of refraction at a ratesubstantially different that an actual velocity v of the stack.Controller 530 may, for example, vary an index of refraction of atransmissive layer so that a transmitted electromagnetic wave is shiftedin frequency by a fixed amount simulating reflection, for example, froma continuously moving surface. Controller 530 may be configured tochange the index of refraction of a transmissive layer cyclically with acycle frequency about equal to or greater than a modulation frequency ofthe incident electromagnetic wave. The index of refraction thetransmissive layer may be dynamically changed so that a portion ofenergy of the transmitted electromagnetic wave has a frequencytranslated outside a pre-defined frequency band of a receiver of themodified electromagnetic wave. Additionally of alternatively, a portionof the energy of the transmitted electromagnetic wave may have afrequency translated outside the frequency band width of the incidentelectromagnetic wave.

Controller 530 may be configured to change the index of refraction atransmissive layer in apparatus 500 at a rate sufficient tosubstantially reduce a temporal phase correlation of the incident andthe transmitted electromagnetic waves. For example, controller 530 mayvary the index of refraction of a transmissive layer according to arandom or pseudo-random pattern such that any temporal phase coherencein the transmitted radiation is reduced or eliminated. In instanceswhere the incident electromagnetic wave has a time-varying frequency [achirp], controller 530 may be configured to dynamically vary the indexof refraction of a transmissive layer with a chirp rate substantiallydifferent than that of the incident electromagnetic wave. Controller 530may be configured to vary index of refraction in a repeating pattern(e.g., in a linear saw tooth pattern). The repeating pattern may beselected to have particular amplitude and frequency components so thatfor at least one incident electromagnetic wave frequency, thetransmitted electromagnetic wave is substantially phase-continuous.

In general, apparatus 500 may be configured to redirect the incidentelectromagnetic wave in a specified direction. Apparatus 500 may includea retro reflector. The retro reflector may, for example, include cornercube structures disposed in the stack of one or more layers.Alternatively or additionally, the one or more layers with controllableindices of refraction may themselves be configured to act as aretroreflector.

In apparatus 500, the one or more layers with controllable indices ofrefraction may include a metamaterial, and/or a broadband metamaterial(e.g., optically-switched metamaterial elements, electrically and/orelectro-magnetically-switched metamaterial elements). The one or morelayers may include one or more materials that exhibit a negative indexrefraction at least under select conditions. The one or more layershaving controllable indices of refraction may form a volume of amaterial that has a change in state that moves through it in response toa spatially varying signal applied by controller 530.

Controller 530 may be configured to apply an optical signal having adefined wavelength and/or intensity, an electrical and/or anelectro-magnetic signal as appropriate to the metamaterial elements toswitch one or more of the layers between different index of refractionstates.

The transmissive layers in apparatus 500 may be partially reflective.The effective position of the reflective surface may be varied so thatthe reflected electromagnetic wave is effectively a sum of reflectionsfrom a first surface and a second surface. Further, controller 530 mayvary the effective position of the reflective surfaces so that arelative amplitude of the reflections from the first and second surfacesis time-dependent (e.g., such that the “new” reflecting surface can“fade in” over the old one, rather than jumping abruptly).

Apparatus 500 may further include an optional reflective surface (e.g.,posterior reflector 550) disposed at or about a posterior surface of thestack of layers having controllable indices of refraction (FIG. 6).Posterior reflector 550 may be configured reflect at least a portion ofthe electromagnetic wave transmitted by the stack of layers. Posteriorreflector 550 may be made of any suitable material including, forexample, metal and/or a photonic bandgap material.

With reference to FIG. 6, controller 530 may be configured to adjust thecontrollable indices of refraction of the one or more layers to changean apparent optical depth and/or angle of the posterior reflectorpresented to the incident electromagnetic wave. Controller 530 may beconfigured to vary an effective optical depth of the posterior reflectoraccording to a random or pseudo-random pattern such that any phasecoherence in the reflected radiation is reduced or eliminated.Controller 530 may be configured to adjust the controllable indices ofrefraction to vary the effective optical depth of the posteriorreflector in a repeating pattern (e.g., a linear saw tooth pattern). Therepeating pattern may be selected to have amplitude and frequencycomponents so that for at least one incident electromagnetic signalfrequency, the reflected electromagnetic signal is substantiallyphase-continuous.

Controller 530 may, for example, vary an effective optical depth of theposterior reflector so that a reflected electromagnetic wave is shiftedin frequency by a fixed amount simulating reflection by a continuouslymoving surface.

Controller 530 may be configured to dynamically vary the controllableindices of refraction of the layers to generate a variable partiallyreflecting surface or a variable partially reflecting Bragg reflector inthe stack so that a reflected electromagnetic signal is effectively asum of a first reflection from the posterior reflector and a secondreflection from the partially reflecting surface or partially reflectingBragg reflector. Controller 530 may be configured to dynamically varythe controllable indices of refraction such that a relative amplitude ofthe first and second reflections is time-dependent (i.e., the “new”reflecting surface can “fade in” over the old one, rather than jumpingabruptly).

Apparatus 500 may further include an optional anterior partiallyreflecting surface (e.g., anterior reflector 560) disposed at or aboutan anterior surface of the stack of layers having controllable indicesof refraction (FIG. 6). Such an apparatus 500 with an optional anteriorreflector or a reflective backing layer may operate as a variablereflector.

The anterior reflector may be configured to reflect at least a firstportion of the incident wave electromagnetic wave, and controller 530may be further configured to dynamically vary the controllable indicesof refraction and to generate a variable partially reflecting surface ora variable partially reflecting Bragg reflector (e.g., Bragg reflector570) in the stack so that a reflected electromagnetic signal iseffectively a sum of a first reflection from the anterior reflector anda second reflection from the partially reflecting surface or partiallyreflecting Bragg reflector. Like posterior reflector 550, anteriorreflector 560 may be made of any suitable material including, forexample, metal and/or a photonic bandgap material.

FIG. 7 shows another apparatus (e.g., apparatus 700), which isconfigured to operate as a variable reflector or phase or time delay.Apparatus 700 may be composed of artificially structured material havingvariable reflective, transmissive or refractive index states that areswitched on or off by an applied field or control signal. The states mayinclude a state in which at least a portion of the material has anegative index of refraction under select conditions. The threshold forswitching between the states switching may vary across the material.External signals of different strengths may be applied to the materialto switch layers of the material to different states as a function ofdepth in the layer, such that the effective position of a reflectingsurface within the material or the effective optical thickness of thematerial at one or more wavelengths is dynamically varied.

Apparatus 700 may, for example, include a block of material 710 madefrom an artificially structured material having a controllable index ofrefraction responsive to an applied field (F), and a controller 730configured to apply a field (F) to the material to induce a spatiallyvarying index of refraction profile in the material and to furthertemporally vary the applied field and the corresponding spatiallyvarying index of refraction profile so as to introduce a time-varyingpath delay d (t) in a modified electromagnetic wave relative to anincident electromagnetic wave.

Material 710 may, for example, be a dielectric material, and the appliedfield F may be a voltage applied across material block 710 by controller730 via electrodes 720. Electrodes 720 may, for example, be made fromconductive semi-transparent materials (e.g., indium oxide). Material mayhave an index of refraction n (x, F), which is a spatially varyingfunction of the applied field F. For example, the index of refraction ofmaterial 710 may have switching threshold between a first value (e.g.,n1) and a second value (n2) with respect to the applied field F. FIG. 7shows, for example, material 710 in which a switching threshold varies(e.g., linearly) as function of depth in the material. An application ofa substantially uniform field F spatially across material 710 which mayresult in a sub-threshold layer of the material with refractive indexstate n1 and another a super-threshold layer of the material withrefractive index state n2.

In other implementations of apparatus 700, material 710 may be opticalmaterial having artificially structured intensity-dependent lightabsorption properties, and the applied field F may be a spatiallyvarying light intensity. Other types of material 710, which areresponsive to other types of fields (e.g., an electrical field, amagnetic field, and/or other energy field), may be deployed. Controller730 may be configured to adjust the spatially varying index ofrefraction profile in the material by applying one or more of anelectric field, an electric current, a magnetic field, mechanicalstrain, ultrasound, and/or light. Material 710 having a controllableindex of refraction may, for example, include optically-switchedmetamaterial elements, electrically and/or electro-magnetically-switchedmetamaterial elements. In such case, controller 730 may, for example, beconfigured to apply an optical signal having a defined wavelength and/orintensity, an electrical and/or electro-magnetic signal as appropriateto adjust the spatially varying index of refraction profile in thematerial. In general, material 710 includes a volume of a material thathas a change in state that moves through it in response to a spatiallyvarying signal applied by the controller.

With renewed reference to FIG. 7, the layers of the material withrefractive index states n1 and n2 may effectively act as a reflective orpartially reflective surface 730. Controller 730 may be configured tovary the applied field (F) to vary the effective position of surface 740to introduce the time-varying path delay d (t) in the path of theincident electromagnetic wave.

As in apparatuses 100, 300 and 500, the time-varying path delay d (t)may, for example, be a substantially pseudo-random or random function oftime or a substantially periodic function of time. The time-varying pathdelay d(t) may be a substantially continuous function of time over atime interval substantially larger than a cycle (1/f) of the incidentelectromagnetic wave. The function may have first or second orderdiscontinuities, which may define the intervening time interval overwhich it is continuous. Exemplary time-varying path delay d (t)functions are linear (e.g., d(t)≈αt+β₀) or quadratic (e.g.,d(t)≈αt²+βt+γ_(o)) in time.

The time-varying phase shift φ(t) may be a selected function such thatthe material has an apparent velocity (≈dφ(t)/dt) and/or an apparentacceleration (≈d²φ(t)/d²t) that are different than its actual velocityand/or acceleration, respectively. In the case of a linearly varyingpath delay d (t) (e.g., d(t)≈αt+β₀, a frequency r of the modifiedelectromagnetic wave may be shifted relative to a frequency f of theincident electromagnetic wave by an amount δf (≈α/2π).

With renewed reference to FIG. 5, at least one of the layers withcontrollable indices of refraction in apparatus 500 may have asubstantially uniform thickness. This feature may, for example, allow atransmitted wavefront shape to remain unchanged. At least one of thelayers may have a thickness of less than about 0.03 of a wavelength ofthe incident electromagnetic wave in the stack. Such a layer thicknessmay correspond to a change in phase of the modified electromagnetic waveof less than about 0.06*π radians. Alternatively or additionally, atleast one of the layers with controllable indices of refraction may havea thickness equal to or larger than about 0.03 of a wavelength of theincident electromagnetic wave in the stack. Such a layer thickness maycorrespond to a change in phase of the modified electromagnetic wave ofabout 0.06*π radians. Further, at least one of the layers withcontrollable indices of refraction may have a thickness equal to orlarger than 0.25 of a wavelength of the incident electromagnetic wave.Such a layer thickness may correspond to a change in phase of themodified electromagnetic wave of about 0.5*π radians.

Controller 730 may be configured to vary index of refraction in arepeating pattern (e.g., in a linear saw tooth pattern). The repeatingpattern may be selected to have particular amplitude and frequencycomponents so that for at least one incident electromagnetic wavefrequency, the transmitted electromagnetic wave is substantiallyphase-continuous. Further, controller 730 may be configured todynamically change the spatially varying index of refraction profile inthe material so that a portion of energy of the modified electromagneticwave has a frequency translated outside a pre-defined frequency band ofa receiver of the modified electromagnetic wave. In instances where theincident electromagnetic wave has a frequency band width, controller 730may dynamically change the spatially varying index of refraction profilein the material so that a portion of energy of the modifiedelectromagnetic wave has a frequency translated outside the frequencyband width of the incident electromagnetic wave. In instances where theincident electromagnetic wave has controller 730 may dynamically changeto the applied field (F) with a substantially different chirp rate thanthat of the incident electromagnetic wave.

Further, controller 730 may be configured to dynamically vary thespatially varying index of refraction profile in the material at a ratesufficient to substantially reduce a temporal phase correlation of theincident and the modified electromagnetic waves. Controller 730 may beconfigured to vary the spatially varying index of refraction profile inthe material according to a pattern having selected amplitude andfrequency components so that for at least one incident electromagneticwave frequency the modified electromagnetic wave is substantiallyphase-continuous (i.e., jumps in phase by full wavelengths). Controller730 also may for example, be configured to vary the spatially varyingindex of refraction profile in the material so that the modifiedelectromagnetic wave is shifted in frequency by a fixed amount relativeto the incident electromagnetic wave to simulate, for example, acontinuously moving surface.

Like apparatus 500, apparatus 700 may further include a posteriorreflective surface or reflector (e.g., reflector 550) disposed on orabout a posterior surface of the material. The posterior reflectivesurface may be configured to reflect at least a portion of the modifiedelectromagnetic wave.

Controller 730 may be configured to change the spatially varying indexof refraction profile in the material to change an apparent opticaldepth and/or angle of the posterior reflector presented to the incidentelectromagnetic signal. Controller 730 may dynamically adjust thespatially varying index of refraction profile in the material togenerate a partially reflecting surface (e.g., surface 740) so that areflected electromagnetic signal is effectively a sum of reflectionsfrom the partially reflecting surface and the posterior reflector.Controller 730 may dynamically adjust the spatially varying index ofrefraction profile in the material such that a relative amplitude of thereflections from the partially reflecting surface and the reflector istime-dependent.

Like in apparatuses 100, 300 and 500, controller 730 in apparatus 700may be configured to modulate an amplitude, a direction, a phase, and/ora frequency of the incident electromagnetic wave according to aninformation carrying signal. Further Like apparatuses 100, 300 and 500,apparatus 700 may also include an electromagnetic radiation detector150. Such an apparatus 700 may be configured to operate as a demodulatorand/or signal correlator. Similarly like apparatus 100, apparatus 700may include a source 160 of the incident electromagnetic wave so thatapparatus 700 can operate as a signal transmitter.

Controller 730 in apparatus 700 may be configured to apply fields sothat the spatially varying index of refraction profile in material 710has a step (e.g., at surface 740) at a substantially uniform depth inthe material. A step in the refractive index at a uniform depth mayyield a reflected or modified wavefront that does not change shape onreflection or transmission. Conversely, controller 730 may be configuredapplying field F so that the spatially varying index of refractionprofile in the material has a step at substantially varying depths inthe material. The spatially varying index of refraction profile in thematerial may have a step at a depth that varies substantially linearlyalong a transverse axis of the material so that the material can operateas a variable prism. Alternatively, the spatially varying index ofrefraction profile in the material may have a step at a depth thatvaries substantially quadratically along a transverse axis of thematerial so that the material can operate as a variable lens.

FIGS. 8-11 show exemplary features of methods 800-1100 for interceptingand modifying electromagnetic waves. The methods may involve deployingapparatuses, for example, of the types described with reference to FIGS.1-7 (apparatuses 100-700) to intercept and modify incidentelectromagnetic waves.

Method 800 may include intercepting an incident electromagnetic wavewith an artificially structured material (e.g., a photonic bandgapmaterial, a metamaterial, a broadband metamaterial, etc.) having anadjustable spatial distribution of electromagnetic parameters (810), anddynamically adjusting the spatial distribution of electromagneticparameters in the material to introduce a time-varying path delay d (t)in a modified electromagnetic wave relative to the incidentelectromagnetic wave 820). Method 900 may include intercepting anincident electromagnetic wave with a stack of one or more layers havingcontrollable reflective properties provided by photonic bandgapmaterials, metamaterial or broadband metamaterial elements therein(910), and dynamically adjusting the controllable reflective propertiesof the one or more layers to present a reflective surface at varyingdepths and/or angles in the stack as a function of time to introduce atime-varying path delay d (t) in a reflected electromagnetic waverelative to the incident electromagnetic wave (920). Method 1000 mayinclude intercepting an incident free space electromagnetic wave with astack of one or more layers of transmissive materials, where the one ormore layers with controllable index of refraction have controllablemetamaterial elements therein (1010), and dynamically adjusting thecontrollable indices of refraction of the one or more layers to at leastpartially transmit an incident electromagnetic wave having a frequencyf, and to introduce a time-varying path delay d (t) in a transmittedelectromagnetic wave relative to the incident electromagnetic wave(1020). Method 1100 may include interposing an artificially structuredmaterial having a controllable index of refraction responsive to anapplied field (F) in a path of an incident free space electromagneticwave (1110), applying a field (F) to the material to induce a spatiallyvarying index of refraction profile in the material (1120) and furthertemporally varying the applied field and the corresponding spatiallyvarying index of refraction profile so as to introduce a time-varyingpath delay d (t) in a modified electromagnetic wave relative to anincident electromagnetic wave (1130).

In method 800, the intercepting material may include a distribution ofdiscrete elements providing the adjustable spatial distribution ofelectromagnetic parameters. The discrete elements may, for example, beman-made photonic bandgap materials, metamaterial elements and/orbroadband metamaterial elements. The spatial distribution ofelectromagnetic parameters in the material may include a selectedspatial profile of at least one electromagnetic parameter in thematerial. The selected spatial profile may, for example, have arectangular step-like shape, a pulse-like shape, or may include asequence of spatial steps or other structures configured to act like aBragg diffraction grating. In three dimensions, a feature of theselected spatial profile (e.g., a step) may have a curved surface thatfocuses or defocuses the incident electromagnetic wave.

In method 800, dynamically adjusting the spatial distribution ofelectromagnetic parameters may include adjusting at least one propertyof the discrete elements to create a selected spatial profile in thevalues of an electromagnetic parameter in the material. Dynamicallyadjusting the spatial distribution of electromagnetic parameters mayinclude modulating an amplitude, a direction, a phase, and/or afrequency of the incident electromagnetic wave according to aninformation carrying signal

Method 800 may include dynamically adjusting the spatial distribution ofelectromagnetic parameters to vary an effective position of the selectedspatial profile and to time-modulate a property (e.g., a phase) of themodified electromagnetic wave. Varying the effective position of theselected spatial profile may include one or more of a translation, arotation, a tilt, a curvature change, a size and/or shape change of theselected spatial profile. Dynamically adjusting the spatial distributionof electromagnetic parameters may include varying an effective positionof the selected spatial profile, for example, in response to an externalsignal, to time-modulate the phase of the modified electromagnetic wave.The effective position of the selected spatial profile may be varied,for example, over a distance smaller than, comparable to, or larger thana wavelength of the incident electromagnetic wave in the material.

In method 800, varying the effective position of the selected spatialprofile at a rate substantially different that an actual velocity v ofthe material and/or at a rate about equal to or greater than amodulation frequency of the incident electromagnetic wave. Further,varying the effective position of the selected spatial profile may besuch that a portion of energy of the modified electromagnetic wave has afrequency translated outside a pre-defined frequency band of a receiverof the modified electromagnetic wave and/or outside a outside thefrequency band width of the incident electromagnetic wave. Method 800may include varying the effective position of the selected spatialprofile according to a random or pseudo-random pattern, a linearrepeating pattern and/or a pattern having selected amplitude andfrequency components so that for at least one incident electromagneticwave frequency the modified electromagnetic wave is substantiallyphase-continuous. The effective position of the selected spatial profilemay be varied at a rate sufficient to substantially reduce a temporalphase correlation of the incident and the modified electromagnetic wavesand/or such that the modified electromagnetic wave is shifted infrequency by a fixed amount relative to the incident electromagneticwave. In instances where the incident electromagnetic wave has atime-varying frequency [a chirp], method 800 may include varying theeffective position of the selected spatial profile with a substantiallydifferent chirp rate than the incident electromagnetic wave.

Method 800 may include adjusting the selected spatial profile of the atleast one electromagnetic parameter in the material to present one ormore effectively reflective or partially reflective surfaces to theincident electromagnetic wave. The selected spatial profile may provideprovides a partial reflection so that the modified electromagnetic waveis effectively a sum of reflections from a first surface and a secondsurface. Method 800 may include dynamically adjusting the spatialdistribution of electromagnetic parameters to vary a property (e.g.,position, shape, or strength) of the selected spatial profile to vary,for example, reflectivity, impedance or properties of the interposedmaterial. The spatial distribution of electromagnetic parameters so thata relative amplitude of the reflections from the first and secondsurface is time-dependent.

A feature (e.g., a step) in the selected spatial profile may define anoutward material layer extending from the feature to an exterior surfaceof the material. Method 800 may include adjusting the spatialdistribution of electromagnetic parameters in the material so thatoutward material layer has a desired interfacial property. For example,properties of the outward material layer may be adjusted so that it hasan electromagnetic impedance η0 matching that of a medium across theexternal surface of the material and/or presents a reflection-freeexternal surface.

In method 800, the intercepting material may include at least one layerswitchable between a transmissive state and a reflective state. Thetransmissive and/or reflective state may be only partially so. The layermay exhibit a negative index of refraction at least under selectedconditions. Method 800 may include applying a control signal to switchthe at least one layer between its states. The control signal may, forexample, be one or more of an electric field, an electric current, amagnetic field, an ultrasonic field, and a light wave. In instanceswhere the intercepting material includes optically-switchedmetamaterial, the control signal may be an optical signal of having adefined wavelength and/or intensity.

Further in method 800, the intercepting material (e.g., a photonicbandgap material, a metamaterial, a broadband metamaterial) may includetransmissive material having a variable refractive index. The materialmay exhibit a negative index of refraction under select conditions. Thenegative index of refraction may provide phase reversal in the modifiedelectromagnetic wave.

Intercepting an incident electromagnetic wave with a stack of one ormore layers having controllable reflective properties in method 900,intercepting an incident free space electromagnetic wave with a stack ofone or more layers of transmissive materials in method 1000, andinterposing an artificially structured material having a controllableindex of refraction in method 1100, may include steps or processes thatare the same or similar to the steps or processes method 800 forintercepting an incident electromagnetic wave with an artificiallystructured material having an adjustable spatial distribution ofelectromagnetic parameters (810). Likewise, dynamically adjusting thecontrollable reflective properties of the one or more layers (910) inmethod 900, and dynamically adjusting the controllable indices ofrefraction of the one or more layers (1010) in method 1000, andinterposing an artificially structured material (1110) and applying andtemporally a field (F) to the material to induce a spatially varyingindex of refraction profile in the material (1120-1130) in method 1100,may include steps of processes that are the same or similar todynamically adjusting the spatial distribution of electromagneticparameters (820) in method 800.

For example, in each of methods 800-1100, the time-varying path delayd(t) may be a substantially pseudo-random or random function of time, ora substantially periodic function of time. The time-varying path delay d(t) may be a substantially continuous function of time over a timeinterval substantially larger than a cycle of the incidentelectromagnetic wave and may have first and/or second orderdiscontinuities. Exemplary time-varying path delays d (t) may be linearor quadratic functions of time over a time interval substantially largerthan a cycle (1/f) of the incident electromagnetic wave. In the methods800 and 1100, varying an effective position of the selected spatialprofile and changing the spatially varying index of refraction profilemay be carried out the in suitable distance increments (e.g., smallerthan about 0.03, about 0.03, or equal to or larger than about 0.25 of awavelength of the incident electromagnetic wave in the material). Thethickness of at least one or the layers in methods 900 and 1000 may alsocorrespond to similar distance increments.

In each of methods 800-1100, the intercepting or interposing materialmay constitute a volume of a material that has a change in state thatmoves through it in response to a spatially varying signal. The materialmay, for example, have electromagnetic parameter (e.g., an index ofrefraction n (x, F)) that is a spatially varying function of an appliedfield F. The electromagnetic parameter may have a switching thresholdbetween a first value and a second value with respect to the appliedfield F. Methods 800-1100 may include applying a field F, which issubstantially uniform across the material to switch portions of thematerial between the first electromagnetic parameter value and thesecond value. The applied field may for example, be electrical fieldand/or a magnetic field. In instances where the material includesoptical material having artificially structured intensity-dependentlight absorption properties, the applied field F may be a spatiallyvarying light intensity. In instances where the material comprisesdielectric material, the applied field F may be a voltage applied acrossthe material.

Each of methods 800-1100 may include adjusting properties of theintercepting or interposing materials time-modulate the modifiedelectromagnetic wave. The properties may be adjusted so that themodified/reflected/transmitted electromagnetic wave is modulated indirection, amplitude, phase and/or frequency according to an externalsignal external command and/or information carrying signal. Theproperties may be adjusted or changed by applying one or more of anelectric field, an electric current, a magnetic field, electromagneticenergy, light, heat, mechanical stress or strain, acoustic and/orultrasound energy to the material. Where the intercepting or interposingmaterials include optically-switched metamaterial elements, the methodsmay include applying an optical signal having a defined wavelengthand/or intensity to change properties of the material. Where theintercepting or interposing materials include electrically and/orelectro-magnetically-switched metamaterial elements, the methods mayinclude applying an electrical or electro-magnetic signal to themetamaterial elements to change properties of the material.

The intercepting or interposing materials may have elements or portions(e.g., layers) that have switchable states including one or more of areflective state a partly reflective state, a transmissive state, apartly transmissive state, a negative refractive index states, and/or avariable index state, etc. Methods 800-100 may include adjusting thematerial properties to switch a material element or portion between itsstates.

Methods 800-1100 may include varying properties of the intercepting orinterposing material (e.g., an effective position of a selected spatialprofile of an electromagnetic parameter, controllable reflectiveproperties of the one or more layers, controllable indices of refractionof the one or more layers, controllable index of refraction, etc.) at arate substantially different that an actual velocity v of the materialand/or at a rate about equal to or greater than a modulation frequencyof the incident electromagnetic wave. Further, the variations in theproperty may be that a portion of energy of themodified/reflected/transmitted electromagnetic wave has a frequencyshifted in by a fixed amount, or a frequency translated outside apre-defined frequency band of a receiver of the modified electromagneticwave and/or outside a outside the frequency band width of the incidentelectromagnetic wave. Methods 800-1100 may include varying or changingthe properties according to a random or pseudo-random pattern, a linearrepeating pattern and/or a pattern having selected amplitude andfrequency components so that for at least one incident electromagneticwave frequency the modified electromagnetic wave is substantiallyphase-continuous. The properties may be varied at a rate sufficient tosubstantially reduce a phase correlation (e.g, temporal phase) of theincident and the modified electromagnetic waves and/or such that themodified electromagnetic wave is shifted in frequency by a fixed amountrelative to the incident electromagnetic wave. In instances where theincident electromagnetic wave has a time-varying frequency [a chirp],method 800 may include varying the properties with a substantiallydifferent chirp rate than the incident electromagnetic wave.

Each of methods 800-100 may further include configuring the interceptingor interposing material to redirect the incident electromagnetic wave ina specified direction, for example, by including a retroreflector in thematerial. The retroreflector may, for example, be corner cube structuresdisposed in the material. Alternatively, properties of the interceptingor interposing material (e.g., index of refraction profiles) may beadjusted so that the material itself acts a retroreflector.

Each of methods 800-100 may also include coupling an electromagneticradiation detector to the intercepting or interposing material andoperating the combination as a demodulator and/or signal correlator.Alternatively or additionally, the methods may also include coupling asource of the incident electromagnetic wave to the intercepting orinterposing material and operating the combination as a signaltransmitter.

Methods 800-1110 may include providing reflective or partiallyreflective surface (e.g., reflector 550) disposed at the posterior oranterior of the intercepting or interposing materials. Alternatively oradditionally, the methods may include adjusting the material propertiesto provide partially reflective surfaces or constructs inside theintercepting or interposing material. The methods may further includeadjusting material properties so that the modified electromagnetic waveis effectively a sum of reflections from a first surface and a secondsurface. The methods may further include adjusting the materialproperties dynamically so that a relative amplitude (or othercharacteristics) of the reflections from the first surface and secondsurfaces are time-dependent. Methods 800-1110 may include dynamicallyadjusting the properties of the material elements, portions or layers tochange an effective optical depth and/or angle of the reflector or aneffective reflective surface presented to the incident electromagneticsignal. Methods 800-1110 may include dynamically adjusting theproperties of the material elements, portions or layers in a repeatingpattern (e.g., a linear saw tooth pattern).

All of the above U.S. patents, U.S. patent application publications,U.S. patent applications, foreign patents, foreign patent applicationsand non-patent publications referred to in this specification and/orlisted in any Application Data Sheet, are incorporated herein byreference, to the extent not inconsistent herewith.

One skilled in the art will recognize that the herein describedcomponents (e.g., steps), devices, and objects and the discussionaccompanying them are used as examples for the sake of conceptualclarity and that various configuration modifications are within theskill of those in the art. Consequently, as used herein, the specificexemplars set forth and the accompanying discussion are intended to berepresentative of their more general classes. In general, use of anyspecific exemplar herein is also intended to be representative of itsclass, and the non-inclusion of such specific components (e.g., steps),devices, and objects herein should not be taken as indicating thatlimitation is desired.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations are not expressly set forth herein for sakeof clarity.

While particular aspects of the present subject matter described hereinhave been shown and described, it will be apparent to those skilled inthe art that, based upon the teachings herein, changes and modificationsmay be made without departing from the subject matter described hereinand its broader aspects and, therefore, the appended claims are toencompass within their scope all such changes and modifications as arewithin the true spirit and scope of the subject matter described herein.Furthermore, it is to be understood that the invention is defined by theappended claims. It will be understood by those within the art that, ingeneral, terms used herein, and especially in the appended claims (e.g.,bodies of the appended claims) are generally intended as “open” terms(e.g., the term “including” should be interpreted as “including but notlimited to,” the term “having” should be interpreted as “having atleast,” the term “includes” should be interpreted as “includes but isnot limited to,” etc.). It will be further understood by those withinthe art that the term “substantially” is used herein generally as a termof approximation, but may be understood to be a term of magnitude ifappropriate in the context of its use. It will be further understood bythose within the art that if a specific number of an introduced claimrecitation is intended, such an intent will be explicitly recited in theclaim, and in the absence of such recitation no such intent is present.For example, as an aid to understanding, the following appended claimsmay contain usage of the introductory phrases “at least one” and “one ormore” to introduce claim recitations. However, the use of such phrasesshould not be construed to imply that the introduction of a claimrecitation by the indefinite articles “a” or “an” limits any particularclaim containing such introduced claim recitation to inventionscontaining only one such recitation, even when the same claim includesthe introductory phrases “one or more” or “at least one” and indefinitearticles such as “a” or “an” (e.g., “a” and/or “an” should typically beinterpreted to mean “at least one” or “one or more”); the same holdstrue for the use of definite articles used to introduce claimrecitations. In addition, even if a specific number of an introducedclaim recitation is explicitly recited, those skilled in the art willrecognize that such recitation should typically be interpreted to meanat least the recited number (e.g., the bare recitation of “tworecitations,” without other modifiers, typically means at least tworecitations, or two or more recitations). Furthermore, in thoseinstances where a convention analogous to “at least one of A, B, and C,etc.” is used, in general such a construction is intended in the senseone having skill in the art would understand the convention (e.g., “asystem having at least one of A, B, and C” would include but not belimited to systems that have A alone, B alone, C alone, A and Btogether, A and C together, B and C together, and/or A, B, and Ctogether, etc.). In those instances where a convention analogous to “atleast one of A, B, or C, etc.” is used, in general such a constructionis intended in the sense one having skill in the art would understandthe convention (e.g., “a system having at least one of A, B, or C” wouldinclude but not be limited to systems that have A alone, B alone, Calone, A and B together, A and C together, B and C together, and/or A,B, and C together, etc.). It will be further understood by those withinthe art that virtually any disjunctive word and/or phrase presenting twoor more alternative terms, whether in the description, claims, ordrawings, should be understood to contemplate the possibilities ofincluding one of the terms, either of the terms, or both terms. Forexample, the phrase “A or B” will be understood to include thepossibilities of “A” or “B” or “A and B.”

With respect to the appended claims, those skilled in the art willappreciate that recited operations therein may generally be performed inany order. Examples of such alternate orderings may include overlapping,interleaved, interrupted, reordered, incremental, preparatory,supplemental, simultaneous, reverse, or other variant orderings, unlesscontext dictates otherwise. With respect to context, even terms like“responsive to,” “related to,” or other past-tense adjectives aregenerally not intended to exclude such variants, unless context dictatesotherwise.

1-120. (canceled)
 121. An apparatus, comprising: a stack of one or more layers of transmissive materials; and a controller coupled to the stack, wherein the one or more layers with controllable index of refraction have controllable metamaterial elements therein, and wherein the controller is configured to dynamically adjust the controllable indices of refraction of the one or more layers to at least partially transmit an incident electromagnetic wave having a frequency f, and to introduce a time-varying path delay d (t) in a transmitted electromagnetic wave relative to the incident electromagnetic wave.
 122. The apparatus of claim 121, wherein the time-varying path delay d (t) is a substantially pseudo-random or random function of time.
 123. The apparatus of claim 121, wherein the time-varying path delay d (t) is a substantially periodic function of time.
 124. The apparatus of claim 121, wherein the time-varying path delay d (t) is a substantially continuous function over a time interval substantially larger than a cycle of the incident electromagnetic wave.
 125. The apparatus of claim 123, wherein the function has a first order discontinuity and/or a second order discontinuity. 126-127. (canceled)
 128. The apparatus of claim 121, wherein the controller is configured to vary the controllable indices of refraction of the one or more layers in a linear repeating pattern.
 129. The apparatus of claim 121, wherein the controller is configured to dynamically adjust the controllable indices of refraction of the one or more layers so that a portion of the energy of the transmitted electromagnetic wave has a frequency translated outside a pre-defined frequency band of a receiver of the transmitted electromagnetic wave and/or the frequency band width of the incident electromagnetic wave.
 130. (canceled)
 131. The apparatus of claim 121, wherein the incident electromagnetic wave has a time-varying frequency and wherein the controller is configured to dynamically vary the controllable indices of refraction in with a substantially different chirp rate than that of the incident electromagnetic wave.
 132. The apparatus of claim 121, wherein the controller is configured to dynamically vary the controllable indices of refraction at a rate sufficient to substantially reduce a phase correlation of the incident and the transmitted electromagnetic waves.
 133. The apparatus of claim 121, wherein the controller is configured to vary the controllable indices of refraction so that the transmitted electromagnetic wave is shifted in frequency by a fixed amount relative to the incident electromagnetic wave.
 134. The apparatus of claim 121, wherein the controller is configured to vary the controllable indices of refraction according to a pattern having selected amplitude and frequency components so that for at least one incident electromagnetic wave frequency the transmitted electromagnetic wave is substantially phase-continuous.
 135. The apparatus of claim 121, further comprising, a posterior reflector disposed on or about a posterior surface of the stack and configured to reflect at least a portion of the transmitted electromagnetic wave.
 136. The apparatus of claim 135, wherein the posterior reflector comprises metal and/or a photonic bandgap material.
 137. The apparatus of claim 135, wherein the controller is configured to adjust the controllable indices of refraction of the one or more layers to change an apparent optical depth and/or angle of the posterior reflector presented to the incident electromagnetic signal.
 138. The apparatus of claim 135, wherein the controller is configured to vary an effective optical depth of the posterior reflector so that a reflected electromagnetic wave is shifted in frequency by a fixed amount.
 139. The apparatus of claim 135, wherein the controller is configured to vary an effective optical depth of the posterior reflector in a repeating pattern.
 140. The apparatus of claim 139, wherein the repeating pattern is selected to have amplitude and frequency components so that for at least one incident electromagnetic signal frequency, the reflected electromagnetic signal is substantially phase-continuous.
 141. The apparatus of claim 135, wherein the controller is configured to dynamically vary the controllable indices of refraction and to generate a variable partially reflecting surface or a variable partially reflecting Bragg reflector in the stack so that a reflected electromagnetic signal is effectively a sum of a first reflection from the posterior reflector and a second reflection from the partially reflecting surface or partially reflecting Bragg reflector.
 142. (canceled)
 143. The apparatus of claim 135, wherein the controller is configured to vary an effective optical depth of the posterior reflector according to a random or pseudo-random pattern. [such that any phase coherence in the reflected radiation is reduced or eliminated].
 144. The apparatus of claim 121, further comprising, an anterior reflector disposed on or about an anterior surface of the stack and configured to reflect at least a first portion of the incident wave electromagnetic wave, and wherein the controller is configured to dynamically vary the controllable indices of refraction and to generate a variable partially reflecting surface or a variable partially reflecting Bragg reflector in the stack so that a reflected electromagnetic signal is effectively a sum of a first reflection from the anterior reflector and a second reflection from the partially reflecting surface or partially reflecting Bragg reflector.
 145. The apparatus of claim 121, wherein the one or more layers with controllable indices of refraction comprise optically-switched metamaterial elements, electrically and/or electro-magnetically-switched metamaterial elements, and wherein the controller is configured to apply one or more of an optical signal having a defined wavelength and/or intensity to change the indices of refraction of the one or more layers.
 146. (canceled)
 147. The apparatus of claim 121, wherein the one or more layers having controllable indices of refraction comprise a volume of a material that has a change in state that moves through it in response to a spatially varying signal applied by the controller.
 148. The apparatus of claim 121, wherein the one or more layers having controllable indices of refraction comprise one or more of a metamaterial, and/or a broadband metamaterial.
 149. The apparatus of claim 121, wherein the one or more layers having controllable indices of refraction comprise one or more materials that exhibit a negative index refraction at least under select conditions.
 150. The apparatus of claim 121, further comprising, an electromagnetic radiation detector coupled to the stack of the one or more layers having controllable indices of refraction, wherein the apparatus is further configured to operate as a demodulator and/or signal correlator.
 151. The apparatus of claim 150, further configured as a demodulator and/or signal correlator. 152-154. (canceled)
 155. The apparatus of claim 121, wherein at least one of the layers having controllable indices of refraction has a thickness such that the phase of the transmitted electromagnetic wave is controlled with an accuracy of better than about 0.06*π radians.
 156. (canceled)
 157. The apparatus of claim 121, wherein at least one of the layers having controllable indices of refraction has a thickness such that the phase of the transmitted electromagnetic wave is controlled with an accuracy of about 0.06*π radians.
 158. (canceled)
 159. The apparatus of claim 121, wherein at least one of the layers having controllable indices of refraction has a thickness such that the phase of the transmitted electromagnetic wave is controlled with an accuracy of about 0.5*π radians.
 160. The apparatus of claim 121, wherein at least one of the layers having controllable indices of refraction has a substantially varying thickness.
 161. (canceled)
 162. The apparatus of claim 121, wherein a first of pair of layers has a thickness that varies substantially linearly along a first transverse axis and a second of the pair of layers has a thickness that varies substantially linearly along a second transverse axis.
 163. The apparatus of claim 121, wherein a first of pair of layers has a thickness that increases along a transverse axis and a second of the pair of layers has a thickness that decreases along the transverse axis.
 164. The apparatus of claim 121, wherein at least one of the layers having controllable indices of refraction has a thickness profile corresponding to a Zernike polynomial (or other polynomial of an orthogonal set of polynomials).
 165. The apparatus of claim 121, wherein at least one of the layers having controllable indices of refraction has a thickness that varies substantially quadratically along a transverse axis. 166-167. (canceled)
 168. The apparatus of claim 121, wherein the controller is configured to adjust the controllable index of refraction of at least one layer in response to an external signal and/or external command.
 169. The apparatus of claim 168, wherein the external signal is an information carrying signal, and wherein the controller is configured to adjust the controllable indices of refraction so that the transmitted electromagnetic signal is modulated in direction, amplitude, phase and/or or frequency according to the information carrying signal, and wherein a source of the incident electromagnetic radiation is coupled to the stack so that the apparatus operates as a signal transmitter. 170-171. (canceled)
 172. The apparatus of claim 121, further comprising, a retroreflector. 173-336. (canceled)
 337. A method, comprising: intercepting an incident free space electromagnetic wave with a stack of one or more layers of transmissive materials, wherein the one or more layers with controllable index of refraction have controllable metamaterial elements therein; and dynamically adjusting the controllable indices of refraction of the one or more layers to at least partially transmit an incident electromagnetic wave having a frequency f, and to introduce a time-varying path delay d (t) in a transmitted electromagnetic wave relative to the incident electromagnetic wave. 338-344. (canceled)
 345. The method of claim 337, wherein the time-varying path delay d (t) is a substantially linear function of time (φ(t)≈αt) so that the transmitted electromagnetic wave has its frequency f shifted relative to a frequency f of the incident electromagnetic wave by an amount δf (=α/2π).
 346. The method of claim 337, wherein dynamically adjusting the controllable indices of refraction of the one of more layers comprises varying the controllable indices of refraction of the one or more layers in a linear repeating pattern.
 347. The method of claim 337, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction of the one or more layers so that a portion of the energy of the transmitted electromagnetic wave has a frequency translated outside a pre-defined frequency band of a receiver of the transmitted electromagnetic wave and/or outside the frequency band width of the incident electromagnetic wave.
 348. (canceled)
 349. The method of claim 337, wherein the incident electromagnetic wave has a time-varying frequency [a chirp rate] and wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction in with a substantially different chirp rate than that of the incident electromagnetic wave.
 350. (canceled)
 351. The method of claim 337, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction so that the transmitted electromagnetic wave is shifted in frequency by a fixed amount relative to the incident electromagnetic wave.
 352. The method of claim 337, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction according to a pattern having selected amplitude and frequency components so that for at least one incident electromagnetic wave frequency the transmitted electromagnetic wave is substantially phase-continuous.
 353. The method of claim 337, wherein the stack further comprises a reflector disposed on or about a posterior surface of the stack and configured to reflect at least a portion of the transmitted electromagnetic wave, and wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction of the one or more layers to change an apparent optical depth and/or angle of the reflector presented to the incident electromagnetic signal.
 354. (canceled)
 355. The method of claim 353, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction of the one or more layers to change an apparent optical depth and/or angle of the reflector presented to the incident electromagnetic signal.
 356. The method of claim 353, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting an effective optical depth of the reflector so that a reflected electromagnetic wave is shifted in frequency by a fixed amount.
 357. The method of claim 353, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting an effective optical depth of the reflector in a repeating pattern.
 358. (canceled)
 359. The method of claim 357, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction to generate a partially reflecting surface so that a reflected electromagnetic signal is effectively a sum of reflections from the partially reflecting surface and the reflector.
 360. (canceled)
 361. The method of claim 353, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting an effective optical depth of the reflector according to a random or pseudo-random pattern.
 362. The method of claim 337, wherein the one or more layers with controllable indices of refraction comprise optically-switched metamaterial elements, and wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises applying an optical signal having a defined wavelength and/or intensity to change the indices of refraction of the one or more layers.
 363. The method of claim 337, wherein the one or more layers having controllable indices of refraction comprise electrically and/or electro-magnetically-switched metamaterial elements, and wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises applying an electrical or electro-magnetic signal to the metamaterial elements to change the indices of refraction of the one or more layers. 364-368. (canceled)
 369. The method of claim 337, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable reflective properties of at least one layer by applying one or more of an electric field, an electric current, a magnetic field, electromagnetic energy, light, heat, mechanical stress or strain, acoustic and/or ultrasound energy to the at least one layer. 370-381. (canceled)
 382. The method of claim 337, wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable index of refraction of at least one layer in response to an external signal and/or external command.
 383. The method of claim 382, wherein the external signal is an information carrying signal, and wherein dynamically adjusting the controllable indices of refraction of the one or more layers comprises adjusting the controllable indices of refraction so that the transmitted electromagnetic signal is modulated in direction, amplitude, phase and/or or frequency according to the information carrying signal. 384-439. (canceled) 